chore(firebaseai): merge same parse logic from developer api and vertexai

[cynthiajoan]

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[natebosch]

Reusing more of the vertex parsing for the developer API looks like it should work out OK. I think as long as we aren't passing arguments like developerParseMode: true it makes sense to merge code paths. Any place where we would need a conditional I think we should continue to lean towards disparate implementations.