feat: Use new segment members api

[kyle-ssg]

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Changes

Frontend for #7861

Replaces current view of identities that belong to a certain segment

How did you test this code?

Please describe.

[vercel]

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Project	Deployment	Actions	Updated (UTC)
flagsmith-frontend-preview	Ready	Preview, Comment	Jun 24, 2026 2:21pm
flagsmith-frontend-staging	Ready	Preview, Comment	Jun 24, 2026 2:21pm

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
docs	Ignored		Jun 24, 2026 2:21pm

[github-actions]

Docker builds report

Image	Build Status	Security report
ghcr.io/flagsmith/flagsmith-api-test:pr-7864	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-e2e:pr-7864	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith:pr-7864	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-api:pr-7864	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-private-cloud:pr-7864	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-frontend:pr-7864	Finished ✅	Results ✅

[github-actions]

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

 1 passed

Details

 1 test across 1 suite
 41.8 seconds
 7b2242d
 🔄 Run: #17782 (attempt 1)

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

 1 passed

Details

 1 test across 1 suite
 45.5 seconds
 7b2242d
 🔄 Run: #17782 (attempt 1)

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

 2 passed

Details

 2 tests across 2 suites
 47.1 seconds
 7b2242d
 🔄 Run: #17782 (attempt 1)

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

 1 passed

Details

 1 test across 1 suite
 1 minute, 1 second
 7b2242d
 🔄 Run: #17782 (attempt 1)

[github-actions]

Visual Regression

19 screenshots compared. See report for details.
View full report

[khvn26]

No notes backend-wise, can confirm the API in #7861 is consumed as expected.