feat: add GPT-5.5 model support and reasoning / verbosity enhancement

[tasoo-oos]

PR Checklist

• Required Checks
  • Have you added type definitions?
  • Have you tested your changes?
  • Have you checked that it won't break any existing features?
• If your PR uses models¹, check the following:
  • Have you checked if it works normally in all models?
  • Have you checked if it works normally in all web, local, and node-hosted versions? If it doesn't, have you blocked it in those versions?
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Summary

Add GPT-5.5 model entries and update GPT-5 reasoning/verbosity parameter handling.

Related Issues

None.

Changes

• Added gpt-5.5 and gpt-5.5-2026-04-23 to the OpenAI model list.
• Added GPT-5 parameter capability markers for none, xhigh, and minimum-medium reasoning effort support.
• Updated reasoning effort and verbosity settings from sliders to segmented controls.
• Clamped invalid reasoning effort values when switching between models with different capabilities.
• Added a noStructuredOutput model flag and skipped JSON schema response formatting for flagged models.
• Added a default verbosity value during database initialization.

Impact

This enables selecting GPT-5.5 and exposes model-specific reasoning options more accurately. Existing GPT-5 model settings may be adjusted to the nearest supported value when a selected model does not support the current reasoning effort. (xhigh -> high, none / low -> mid)

Internally, this feature still uses integer-based value mapping.

Demo

GPT-5.2 ~ GPT-5.5

GPT-5.1

GPT-5

GPT-5.4 Pro

Footnotes

1. Modifies the behavior of prompting, requesting, or handling responses from AI models. ↩

2. Over 80% of the code is AI generated. ↩