fix(ai): firebase_ai server template image inputs passed as InlineDataPart were serialized as normal generative inlineData

[Lyokone]

Description

Fixes firebase_ai server template requests so InlineDataPart values in template inputs are serialized as inline media variables instead of generative-content inlineData parts. This lets image inputs passed to TemplateGenerativeModel.generateContent and streaming/history template calls reach the server template as base64 media content with the expected MIME type.

A unit regression test covers passing an InlineDataPart screenshot input through generateContent.

Related Issues

• Fixes Firebase_AI: Hallucinations with server-side template usage #18326

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.

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