feat(MCP): Set up Sentry error reporting

[emyller]

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Changes

Contributes to #7771

Set up Sentry in the MCP server for error reporting.

How did you test this code?

New tests.

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3 Skipped Deployments

Project	Deployment	Actions	Updated (UTC)
docs	Ignored		Jun 25, 2026 10:38pm
flagsmith-frontend-preview	Ignored		Jun 25, 2026 10:38pm
flagsmith-frontend-staging	Ignored		Jun 25, 2026 10:38pm

[github-actions]

Docker builds report

Image	Build Status	Security report
ghcr.io/flagsmith/flagsmith-api-test:pr-7879	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-e2e:pr-7879	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-frontend:pr-7879	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-api:pr-7879	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith:pr-7879	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-private-cloud:pr-7879	Finished ✅	Results ✅

[github-actions]

Playwright Test Results (oss - depot-ubuntu-latest-16)

 1 passed

Details

 1 test across 1 suite
 41.7 seconds
 7266d75
 🔄 Run: #17840 (attempt 1)

Playwright Test Results (oss - depot-ubuntu-latest-arm-16)

 1 passed

Details

 1 test across 1 suite
 44.7 seconds
 7266d75
 🔄 Run: #17840 (attempt 1)

Playwright Test Results (private-cloud - depot-ubuntu-latest-16)

 3 passed

Details

 3 tests across 3 suites
 34 seconds
 7266d75
 🔄 Run: #17840 (attempt 1)

Playwright Test Results (private-cloud - depot-ubuntu-latest-arm-16)

 2 passed

Details

 2 tests across 2 suites
 1 minute, 13 seconds
 7266d75
 🔄 Run: #17840 (attempt 1)

[github-actions]

Visual Regression

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