.. instead of a FlatStringReader. This is in preparation for reusing
the regexp parser directly from the JS parser, which uses different
string types (AstRawString instead of heap Strings).

Drive-by: Hide parser internals in the .cc file.

Bug: v8:896
Change-Id: I06bd08f2ef5fd7a5e9812c123d88b89cacf5d864
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/3101488
Commit-Queue: Patrick Thier <pthier@chromium.org>
Auto-Submit: Jakob Gruber <jgruber@chromium.org>
Reviewed-by: Patrick Thier <pthier@chromium.org>
Cr-Commit-Position: refs/heads/main@{#76365}