You are trying to overcomplicate this. an mcu has a processor. A processor has a processor. there have been processors that you can find on both an MCU and an SOC that is linux capable (not just rtos or uclinux). Its like having a few horsepower motor on your lawnmower and also having the same or similar on your golf cart. Or like having a school made of bricks or a house made of the same style/brand of bricks. Dont get hung up on that. Particularly with the rest of your question which has nothing to do with the processor used in the chip at all.
Atmel wants to make an MCU, so the either create, reuse or buy a processor, they have at least one if not more processors that are their IP but they choose to buy someone elses IP. Now they want to wrap some logic around it they can use some of their own ip or buy some. Each major block is a new discussion. Do they make their own uart from scratch, do they take a uart they created years ago and re-use that, or do they buy a uart. Do they make an ADC from scratch, do they take an ADC they made years ago and use that, do they purchase an ADC design from someone and use that. Repeat for every major or minor block in the design. Just like Honda making a car, which parts are they going to make themselves and which parts are they going to buy, and does that have any relevance to a design they made years ago, or a truck sized vehicle vs a compact car, they both have four wheels, an engine and some seats, in some cases may share some components and others completely incompatible components. but its the same story, do we make a seat, use one we already have, buy one. do we make a rear view mirror, use one we already have from a prior design, or buy them from someone else. the rear view mirror decision likely has nothing to do with the seat decision.
Registers its just a term a thing you write/store some information in. A uart has registers to make it work. A processor usually has registers to make it work. An ADC usually has registers to make it work. Consider each of these blocks as separable.
A processor core is a logic blob that is programmable in the sense that it has a set of rules and its primary interface is a memory bus where it is the master, it expects to find when fetched instructions per its design that tell it what to do, up to the chip vendor to wire that up to something that will feed it instructions. It may have some interrupt lines and a few other things but its primary interface is that memory bus. The "registers" inside are part of the design accessed by the processor internals and not generally memory mapped.
A uart is a logic blob that that is programmable, it has some sort of a memory/interface bus where it is typically a slave. It also has some other signals that go off chip, RX, TX, RTS, CTS, DTR...The registers inside the uart are addressable through the interface bus and are used to make the uart operate. It is up to the chip vendor to connect this bus in a way that it fits into the address space of a bus master that directly or indirectly can write/read the registers in the uart to make it operate. It is programmable in the sense that programming the registers per its spec makes it operate.
An ADC is a logic blob that is sometimes found to be programmable, sometimes not. The converter itself isnt usually. But when used in a chip that does more than just ADConversions there will be an additional logic blob wrapped around the ADC to make it programmable and that logic blob will have some sort of an interface bus where it is a slave. It is up to the chip vendor to connect this bus to a bus master that in some way is capable of programming the ADC to do something.
This isnt limited to ARM based microcontrollers. You look inside an intel x86 processor there is third party IP in there not invented nor created by intel, a lot of it may be but not all. Same goes for pretty much everyone else.
Processor based chips are just cars with seats and an engine and wheels that were per that design sourced from somewhere and then interfaced to each other using more IP from someone be it in house or not.
For any of these chips each IP blob has documentation uart documentation, adc documentation, processor core documentation. Sometimes the license agreement prevents the chip vendor from publishing the documentation and you have to get a driver from them in some sort of board support package or SDK in some form, countless examples of this with chip vendors you have heard of from atmel to intel to zilog. Likewise there are license agreements or common practices that guide what parts the chip vendor is going to document and how and what parts not. So generally but not always when you have specifically an ARM or MIPS core as part of a design. The processor documentation as you should generally do always, is from the processor vendor so ARM, MIPS, etc. The uart, the ADC, and some others be they in house or purchased IP are generally in the chip vendors documentation. The chip vendor ideally created the address space within the rules of the various ip, so the chip vendor often documents where in the processors address space each logic blob lives, then you go to the documentation for that logic blob to see what the individual control interfaces do, registers or memory mapped memory. Not always true though esp with uarts, you sometimes find this is a 16550 compatible and you have to go find a 16550 document from someone else and connect the dots on your own. The raspberry pi includes for example other peripherals where they basically say this is just an arm purchased blob go to arm for this, or there is a blob here and we wont show you how it works (but we publish the linux driver for it and if eager you can reverse engineer from that).
With an Atmel now Microchip ARM based product you (generally) go to arm to get info on the processor core, its general purpose registers as well as the very few internal to the core peripherals like the systick timer if present. The uart, the gpio, the address space, spi, i2c, etc are going to be in one or more Atmel documents for that part, they cover the register specs for those peripherals.
As far as how many documents it takes from the chip vendor that is very much chip vendor and over time family or product line specific. Some chip vendors as with some customers like the board design specific stuff in one document usually called a datasheet. Pinouts, electrical stuff, etc. And the other documents cover the uart register specs and such. Some designs are such that they reuse the same core components. if you have a uart then here is the register spec all of our uarts are the same. so there will be a manual for all of the chips peripherals and maybe the processor or maybe the processor core itself is in a separate manual. In some cases with that design solution, the peripherals if present are always at the same address or they are not. The one I am thinking of you find the board design stuff in the datasheet along with the address map, but the rest of the information for programmers is in the family reference manual, so you need at least those two documents.
And there are of course vendors that either make bad documents with holes as sad habit, or some that intentionally do not provide documentation without an NDA, for fear that a competitor will make a clone perhaps, or just a habit for that company that goes way back. Sometimes those closed book companies do very well sometimes that causes them pain. Broadcom and allwinner seem to do okay, allwinner docs tend to get left about by chip vendors and I guess they dont get punished, but other companies you will get called out for that possibly with a financial or other punishment. Its all in the legal agreement.
There are a few perpherals where there is only one or two designs and everyone just buys it, and despite being undocumented looking at linux/unix drivers can see that everyone uses the same IP.
Way more than you asked for but could tell from your question you were off on the wrong path.
Generally the ARM stuff is not in the chip vendor stuff, so no you wouldnt find it there. Sometimes (rare) the chip vendor will re-publish an arm document in whole or in part. Better to get it from arm directly. In the case of a cortex-m the arm peripherals on core are at fixed/well known addresses. For the cortex-a, and older arm11, arm10, arm9...The chip vendor straps a peripheral base address in the address space they have designed for that product and the internal arm peripherals if any are based off of that. so you can find two products likely from different vendors with the same core but the memory mapped peripherals inside are at different addresses for this reason. (in the technical reference manuals for the various arm cores).
