[Gardener] Revert "[bookmarks] Clear last used parent cache when adding bookmark fails"

This reverts commit eedc2f13b941728513b9dff5d4d9910f94a1c972.

Reason for revert: This causes a presumbit failure seen at:
https://ci.chromium.org/ui/p/chromium/builders/ci/linux-presubmit/28441/overview
saying that:
tools/metrics/actions/actions.xml is not up to date or is not formatted correctly; run tools/metrics/actions/extract_actions.py to fix

Original change's description:
> [bookmarks] Clear last used parent cache when adding bookmark fails
>
> Bug: 415333373
> Change-Id: Ib810fcdb75e190bb8f88411787cd2aa192b06810
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6598838
> Reviewed-by: Brandon Wylie <wylieb@google.com>
> Reviewed-by: Sky Malice <skym@chromium.org>
> Commit-Queue: Evan Luo <evanluo@google.com>
> Cr-Commit-Position: refs/heads/main@{#1467115}

Bug: 415333373
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Change-Id: Ife422b5d0bd4813b0706d22c6ebac237c6d99a1e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6604818
Reviewed-by: Sky Malice <skym@chromium.org>
Commit-Queue: Sky Malice <skym@chromium.org>
Owners-Override: David Baron <dbaron@chromium.org>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Auto-Submit: David Baron <dbaron@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1467168}