fix: removed api logout call

[Zaimwa9]

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Changes

As logging out from the API invalidate the user token, we reverted to not calling the API when logging out from dashboard

How did you test this code?

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Project	Deployment	Actions	Updated (UTC)
flagsmith-frontend-preview	Ready	Preview, Comment	May 7, 2026 7:35am
flagsmith-frontend-staging	Ready	Preview, Comment	May 7, 2026 7:35am

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
docs	Ignored		May 7, 2026 7:35am

[github-actions]

Docker builds report

Image	Build Status	Security report
ghcr.io/flagsmith/flagsmith-api-test:pr-7448	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-e2e:pr-7448	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-api:pr-7448	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith:pr-7448	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-private-cloud:pr-7448	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-frontend:pr-7448	Finished ✅	Results ✅

[github-actions]

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

 11 passed

Details

 11 tests across 8 suites
 42.9 seconds
 1655d81
 🔄 Run: #16585 (attempt 1)

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

 11 passed

Details

 11 tests across 8 suites
 46.8 seconds
 1655d81
 🔄 Run: #16585 (attempt 1)

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

 2 passed

Details

 2 tests across 2 suites
 1 minute, 4 seconds
 1655d81
 🔄 Run: #16585 (attempt 1)

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

 1 passed

Details

 1 test across 1 suite
 47.8 seconds
 1655d81
 🔄 Run: #16585 (attempt 1)

[github-actions]

Visual Regression

16 screenshots compared. See report for details.
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[matthewelwell]

For additional context, this is being done because the token is presented to users in their account settings as an 'API key'. Until we build properly scoped user API keys, or just force everyone to use org-level API keys, we cannot invalidate these tokens on logout.