Partially Reland "Automatically generate libcxx headers as a hook."

This reverts commit 920adc8f1cf65a63043776e2192bd6ce5819cd31.

Reason for revert: Safe partial revert which fixes the bug introduce in
the original commit.

Bug: 432582032
Original change's description:
> Revert "Automatically generate libcxx headers as a hook."
>
> This reverts commit f757979abb319cab03a3a040b5fd288f06edf6ad.
>
> Reason for revert:
> This broke Cider-G
> https://chromium-review.googlesource.com/c/chromium/src/+/6768520/comments/13bb2d1d_3e90a250
>
> Bug: 432582032
> Original change's description:
> > Automatically generate libcxx headers as a hook.
> >
> > I'm explicitly choosing not to do anything with it yet, to make for a simpler rollback if it doesn't go well.
> >
> > In a follow-up CL, I will delete libcxx_headers.gni and replace all
> > references to it to the generated version.
> >
> > Bug: 432582032
> > Change-Id: I6a6a6964d84cab9d121fbfe0da227c8237953f0c
> > Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6768520
> > Auto-Submit: Matt Stark <msta@google.com>
> > Reviewed-by: Junji Watanabe <jwata@google.com>
> > Reviewed-by: Takuto Ikuta <tikuta@chromium.org>
> > Commit-Queue: Matt Stark <msta@google.com>
> > Reviewed-by: Brian Ryner <bryner@google.com>
> > Cr-Commit-Position: refs/heads/main@{#1494567}
>
> Bug: 432582032
> No-Presubmit: true
> No-Tree-Checks: true
> No-Try: true
> Change-Id: I24d90a747e6bd37353856d13b34c797f9ba9a72c
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6805053
> Commit-Queue: Takuto Ikuta <tikuta@chromium.org>
> Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
> Cr-Commit-Position: refs/heads/main@{#1494660}

Bug: 432582032
Change-Id: Ia6ff26c7248a90b75ed25fe9fb0fc53e69535782
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6808195
Reviewed-by: Takuto Ikuta <tikuta@chromium.org>
Commit-Queue: Matt Stark <msta@google.com>
Cr-Commit-Position: refs/heads/main@{#1495212}