Add Synthorai provider

[cuihuan]

Name of model: Synthorai (gateway provider, not a single model — routes to 122 models)
Model creator: Synthorai
Link to model: https://synthorai.io/docs

Note: this is a request to add Synthorai as a provider option (like the existing OpenRouter/Requesty/TrustedRouter entries), not a single model — it's an OpenAI/Anthropic-compatible gateway to 122 models across 11 upstream providers (Claude, GPT, Gemini, GLM, Kimi, DeepSeek, Qwen, etc.) at direct upstream pricing. Base URL https://synthorai.io, standard Bearer auth. Free tier available for testing (10 calls / up to $1, no card).

[cuihuan]

Belated but important disclosure: I'm affiliated with Synthorai — this request adds support for our own product, it isn't me reporting demand from elsewhere. I should have said so in the original post; flagging it now so the ask is judged on its merits with that context on the table.

No expectation of priority attached. Happy to do the implementation work myself, and equally happy to take "not now" for an answer.