> I'll end up with this state, where `E` remains untouched?

Can't, because a commit's hash takes into account the parent hashes.

Haven't used --update-refs, but reading it, it should result in your third graph. So,

> is there a way to get `git rebase` to have the same behavior?

is already the case.

It won't result in the third graph on its own as E isn't reachable from D, but it could if you first merged D and E together and then used --update-refs with --rebase-merges. You could then just discard the merged branch and only take care of D' and E' on their own (and since you don't care about the merged branch, you don't have to care about resolving conflicts while preparing it either).

> Haven't used --update-refs, but reading it, it should result in your third graph.

I don't think it does. I tried locally:

  mkdir test; cd test; git init
  touch a; git add a; git commit -m 'a'
  touch b; git add b; git commit -m 'b'
  touch c; git add c; git commit -m 'c'
  git checkout -b branched-feature HEAD~
  touch d; git add d; git commit -m 'd'
  git checkout main
  echo 'change' > b; git add b; git commit -m 'fix b'
  git rebase -i --root --update-refs

  * commit (HEAD -> main)
  |
  |     c
  |
  * commit 
  |
  |     b
  |
  | * commit (branched-feature)
  | |
  | |     d
  | |
  | * commit
  |/  
  |       b
  |
  * commit 
  
        a

  * commit (branched-feature)
  |
  |     d
  |
  | * commit (HEAD -> main)
  |/
  |       c
  |
  * commit
  |
  |     b
  |
  * commit 
  
        a

Unless E remained untouched because it was not rewritten, and ended up staying parented on B instead of getting reparented onto B'.

Which is usually not what you want; most of the time you want E', which is E reparented onto B'. But sometimes you want E to remain untouched and stay parented on the original B. Depends on the situation.