fix(ai): reuse a persistent http.Client in HttpApiClient

[SelaseKay]

Description

HttpApiClient fell back to http.post / Request.send() when no client was injected. Those helpers create and close an http.Client per call, which tears down the TCP/TLS connection and forces a fresh handshake on every generateContent.

This keeps a long-lived http.Client on each HttpApiClient (httpClient ?? http.Client()) so keep-alive reuse can work for the lifetime of the model. Injected clients are unchanged. idleTimeout is still the dart:io default (15s); apps that need a longer pool can already pass a tuned IOClient via FirebaseAI.generativeModel(httpClient: …).

Related Issues

• Fixes 🚀 [firebase_ai] HttpApiClient creates a new http.Client per request — no TCP/TLS connection reuse #18602

Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• My PR includes unit or integration tests for all changed/updated/fixed behaviors (See Contributor Guide).
• All existing and new tests are passing.
• I updated/added relevant documentation (doc comments with ///).
• The analyzer (melos run analyze) does not report any problems on my PR.
• I read and followed the Flutter Style Guide.
• I signed the CLA.
• I am willing to follow-up on review comments in a timely manner.

Breaking Change

• Yes, this is a breaking change.
• No, this is not a breaking change.

Test plan

• flutter test test/client_test.dart in packages/firebase_ai/firebase_ai (3 tests passed)
• Confirm default generateContent still works against a real backend
• Optional: two back-to-back calls within 15s should reuse the connection (no extra handshake)

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