The difference between bash and zshell are minimal. They are both a "shell" that run in the terminal. A shell is what allows you to run commands in the terminal. It has its own language called bash or alternatively shell scripting. If you have ever typed ls or cd in a terminal, you are using bash commands to move around or look at things in the terminal. (The terminal itself is just the little oftentimes black square you type into.) It doesn't really matter which one you pick at this point, but you should just go with one.
If you pick bash, the files that interact with it will be under your home directory, the error tells you exactly where. /Users/eyan/.bash_profile the .bash_profile sets some configurations for bash.
If you pick zshell, the files will instead of starting with '.bash_ they'll start with .zsh the most common one will be .zshrc and it will be in the same home directory. So /Users/eyan/.zshrc will be the config file for zshell.
Pick one and just stay with it for now.
In either case, you want to initialize conda.
In your terminal, if you type:
which conda
It should tell you where your conda is installed. If you get a bunch of nonsense running that, try which python. One of them should give you something like this output:
/Users/eyan/opt/anaconda3/bin/python
Change the python in that line to activate and add the command source to the front. So type:
source /Users/eyan/opt/anaconda3/bin/activate
Once you've done that type:
conda init
All of this is done in the terminal. And that should add a bunch of stuff to your shell profiles. (That's those files in your home directory like .bash and .zshrc.)
If you close and reopen your terminal or type EXEC $SHELL in the same terminal window, you should be able to use conda.
You can also see what was added to your bash (or zsh) profiles by typing:
cat /Users/eyan/.bash_profile
(Or if you've chosen zshell, run cat /Users/eyan/.zshrc)
You'll see that conda added quite a few lines to it. Don't worry about what those lines do for now, but you can see them there.