Tweak a few names, remove a few GetIsolate calls, other minor
usability refactors.

It may be worth taking a closer look at the impl in the future,
currently the design choices don't seem ideal (see the added TODO
on top of the class).

The reland is unchanged from the original CL.

Bug: v8:12161
Change-Id: I9971f7f2fb08b7a1ec2d57b2a0e4accdc11191ca
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/3568444Reviewed-by: Leszek Swirski <leszeks@chromium.org>
Commit-Queue: Jakob Linke <jgruber@chromium.org>
Cr-Commit-Position: refs/heads/main@{#79759}