[0.81] Clean up feature flag `preventShadowTreeCommitExhaustionWithLocking` and move to `preventShadowTreeCommitExhaustion` (still experimental)

[cortinico]

Target Branch

0.81

Link to commit or PR to be picked

facebook/react-native#52862

Description

After further experimentation from the Reanimated team, we realized that the fix introduced with the feature flag preventShadowTreeCommitExhaustionWithLocking was not correct. @rubennorte worked on a different fix that I've picked on this PR.

We only need to merge the PR against the release branch:

• [0.81] Clean up feature flag preventShadowTreeCommitExhaustionWithLocking facebook/react-native#52862

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[motiz88]

Merged facebook/react-native#52862.