Issue #3508886: Filter loaded models list by supportedGenerationMethods and name patterns

Giorgi Jibladzerequested to merge
issue/gemini_provider-3508886:3508886-filter-the-loaded into 1.x

Rewrites getConfiguredModels() filtering to use the API's supportedGenerationMethods as the primary signal, combined with name-based exclusion patterns for specialized models (imagen, veo, TTS, native-audio, robotics, computer-use, deep-research, aqa).

Chat drops from ~44 to ~27 models, text_to_image from ~30 to ~4.

Co-Authored-By: Claude Opus 4.6 noreply@anthropic.com

Closes #3508886

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