### What problem does this PR solve?
Closes#14703
`GoogleModel.CheckConnection` currently returns a hardcoded `no such
method` error even though the Google Go driver already supports
`ListModels`. This makes provider connection checks fail regardless of
whether the configured API key can list Google models.
This PR makes `CheckConnection` call `ListModels`, adds a small API-key
guard for nil, empty, and whitespace-only keys, and keeps `ListModels`
useful by following paginated Google model responses.
### What stays unchanged
* Google model listing still uses the Google GenAI SDK with
`genai.BackendGeminiAPI`.
* Model names still come from `models.Items[*].Name`.
* `Balance`, `Encode`, chat, streaming, provider config, and factory
wiring are unchanged.
### Tests and validation
Added focused unit coverage for:
* `CheckConnection` delegating to `ListModels` and returning its error
* nil, missing, empty, and whitespace-only API key validation
* model-name passthrough from the list-models adapter
* paginated model listing, empty-result preservation, and next-page
error propagation
Validated current PR head `17ceef43515ba8c46c254dd349b9085bf26dcbea`
locally with Go 1.25.0:
* `go test ./internal/entity/models -run
'TestGoogleModel|TestCollectGoogleModelNames' -count=1 -v` - PASS
* `go test ./internal/entity/models -count=1` - PASS
* `go test -race ./internal/entity/models -count=1` - PASS
* `gofmt -w internal/entity/models/google.go
internal/entity/models/google_test.go` - PASS, no diff
* `git diff --check` - PASS
### Type of change
* [x] Bug Fix (non-breaking change which fixes an issue)
Co-authored-by: Jin Hai <haijin.chn@gmail.com>
