Upgrade Sentry to v10 with React integration

[RichDom2185]

Description

Migrates from @sentry/browser to @sentry/react with better integration for React-specific things like client side navigation with React Router, etc.

Also adds sourcemaps for better error messages.

Supersedes #3220.

Type of change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update
• Code quality improvements

How to test

Checklist

• I have tested this code
• I have updated the documentation

[coveralls]

Pull Request Test Coverage Report for Build 17016265885

Details

• 9 of 35 (25.71%) changed or added relevant lines in 11 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-0.01%) to 43.452%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
rsbuild.config.ts	0	2	0.0%
src/commons/application/ApplicationWrapper.tsx	0	2	0.0%
src/pages/achievement/Achievement.tsx	0	3	0.0%
src/pages/leaderboard/Leaderboard.tsx	0	3	0.0%
src/pages/leaderboard/subcomponents/ContestLeaderboardWrapper.tsx	0	3	0.0%
src/index.tsx	0	13	0.0%

Totals
Change from base Build 17016244503:	-0.01%
Covered Lines:	20658
Relevant Lines:	49739

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💛 - Coveralls

[sayomaki]

LGTM!