fix: browser storage (localStorage) is unreliable: api should fail-safe

[slorber]

Motivation

Storage APIs must be considered as unreliable, and Docusaurus should keep working even if all storage apis throw errors.

See also #6036

Have you read the Contributing Guidelines on pull requests?

yes

Test Plan

only tested locally by making lower-level apis throw => Docusaurus stays accessible

[netlify]

✔️ [V2]

🔨 Explore the source changes: cb46e8d

🔍 Inspect the deploy log: https://app.netlify.com/sites/docusaurus-2/deploys/61a9013b79c4bc0008672e26

😎 Browse the preview: https://deploy-preview-6040--docusaurus-2.netlify.app

[github-actions]

⚡️ Lighthouse report for the changes in this PR:

Category	Score
🟢 Performance	93
🟢 Accessibility	98
🟢 Best practices	100
🟢 SEO	100
🟢 PWA	95

Lighthouse ran on https://deploy-preview-6040--docusaurus-2.netlify.app/

[github-actions]

Size Change: +263 B (0%)

Total Size: 645 kB

Filename	Size	Change
website/build/assets/js/main.********.js	477 kB	+263 B (0%)

ℹ️ View Unchanged

Filename	Size
website/.docusaurus/globalData.json	38.3 kB
website/build/assets/css/styles.********.css	99.5 kB
website/build/index.html	29.5 kB

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