Tests: Improve REST API test isolation

[sirreal]

Summary

• Isolates REST authentication flags, block registrations, widget factories, sidebar state, theme features, script globals, and mocked URL validation fixtures.
• Keeps the changes confined to PHPUnit tests and fixtures.

Verification

• 50 consecutive randomized REST API group runs passed; each completed 3,550 tests.
• Replayed the original failing seed and focused contaminator/consumer cases during diagnosis.
• PHP syntax checks passed for every changed PHP file.
• git diff --check passed.

Trac: https://core.trac.wordpress.org/ticket/65893