chore: get auth logic in sync with the VSCE

[tatomyr]

What/Why/How?

Synced auth logic with the latest changes in VSCE

Reference

Related: https://github.com/Redocly/redocly/pull/18048

Testing

Screenshots (optional)

Check yourself

• Code changed? - Tested with Redoc/Realm/Reunite (internal)
• All new/updated code is covered by tests
• New package installed? - Tested in different environments (browser/node)
• Documentation update considered

Security

• The security impact of the change has been considered
• Code follows company security practices and guidelines

[changeset-bot]

⚠️ No Changeset found

Latest commit: 79f5f22

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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[github-actions]

Command	Mean [s]	Min [s]	Max [s]	Relative
redocly lint packages/core/src/benchmark/benches/rebilly.yaml	1.425 ± 0.017	1.396	1.444	1.00
redocly-next lint packages/core/src/benchmark/benches/rebilly.yaml	1.430 ± 0.025	1.389	1.467	1.00 ± 0.02