perf(frontend): reduce api requests for non-logged-in enviroment

[syuilo]

What

Resolve #14805

Why

Additional info (optional)

Checklist

• Read the contribution guide
• Test working in a local environment
• (If needed) Add story of storybook
• (If needed) Update CHANGELOG.md
• (If possible) Add tests

[github-actions]

このPRによるapi.jsonの差分
差分はありません。
Get diff files from Workflow Page

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 51 lines in your changes missing coverage. Please review.

Project coverage is 39.92%. Comparing base (7b9c884) to head (ec73511).
Report is 2 commits behind head on develop.

Files with missing lines	Patch %	Lines
packages/frontend/src/server-context.ts	0.00%	22 Missing and 1 partial ⚠️
...ages/backend/src/server/web/ClientServerService.ts	0.00%	13 Missing ⚠️
packages/frontend/src/pages/note.vue	0.00%	8 Missing ⚠️
packages/frontend/src/pages/clip.vue	0.00%	7 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop   #15001      +/-   ##
===========================================
- Coverage    39.97%   39.92%   -0.05%     
===========================================
  Files         1561     1562       +1     
  Lines       197358   197406      +48     
  Branches      3609     3606       -3     
===========================================
- Hits         78888    78817      -71     
- Misses      117864   118015     +151     
+ Partials       606      574      -32     

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