Support model selection via user profile

[jschoedl]

What and why

Make it possible to set the LLM model via the user profile. After this is added in the frontend, this would make it easier to demonstrate that we're able to deal with different models. (Follow-up to #111)

Proposed approach

• add to the profile in the spec:
  • id of the selected model (proposal: gemini-3.1-flash-lite or logos for the predefined models, openai for any OpenAI LLM)
  • optional: BaseURL / key for the model
  • optional: reasoning_effort (this is not supported for all LLMs, but e.g. Logos would support low/medium/high)
• we should probably store the model key encrypted (like the password)

Affects API?

• Yes → api/openapi.yaml will need updating before implementation
• No