First things first: You do not want to do a git pull at this point. You could recover even if you did, but it will be taking you in the wrong direction[1].
So the steps you followed correctly recovered the changes that had been committed during the previous rebase attempt - which may be useful.
But that's not the same as putting git back into a rebasing state. There are other things going on - e.g. git is managing a todo list of patches representing the original commits.
As far as I know, there isn't really a way to restart a rebase that's been aborted. But you can approximate it using rebase --onto.
(a) from the tip of the old rebase (where you had reset to) create a tag
(b) reset back to where the branch was before the rebase. (You can again find this in the reflog; it's where the rebase --abort sent you.)
(c) now, supposing you have
x -- A -- B -- C -- D <--(branch)
\
x -- x -- o <--(master)
\
A' -- B' <-rebase_tag
where rebase_tag is the tag you created at the tip of the old rebase attempt, so A' is the rewrite of A, B' is the rewrite of B, and you still need to rewrite C and D.
What you want to do is rewrite C and D onto B'. So
git rebase --onto rebase_tag branch~2 branch
Here, branch~2 can be replaced with any expression that resolves to B (the last of the original commits that has been rewritten in the previous rebase attempt).
Of course, if the work related to the original rebase attempt is minimal - if it didn't take much time and there wasn't a lot of complicated merge resolution going on - you could just restart from scratch. Even doing that, you could use the "old rewritten commits' as reference when resolving conflicts.
But assuming it's clear to you how to calculate the expression for the --onto parameter, the above is probably the easiest way to "restart' the rebase.
[1] The thing to understand here is, certain git commands give very detailed/specific advice; but that advice is written to address the common use cases, where you've done certain things they assume a new user would usually do. It's fine that you do things that don't fit those assumptions, but they assume that anyone who does knows enough to not need the specific/detailed advice.
So what's happened is, you've done something outside those assumptions, so the pull advice doesn't apply; if you follow it, you'll be heading further in the wrong direction. Not that you couldn't still recover - you could - but it would be even more confusing.
