chore(deps): bump infer CLI v0.117.0 -> v0.117.1, infer-action v0.9.1 -> v0.11.1

[ghost]

Summary

Centralized-config changes in one PR:

1. Adds/updates .github/workflows/infer.yml as a thin caller of the org reusable workflow
   inference-gateway/.github/.github/workflows/infer.yml@v0.5.3,
   wiring the @infer bot (inference-gateway/infer-action) into this repo.
2. Bumps this repo's Flox infer pin (.flox/env/manifest.toml) to
   v0.117.1 (the latest inference-gateway/cli release) and
   refreshes .flox/env/manifest.lock.
3. Regenerates the committed .infer/ config with infer init --overwrite --skip-migrations
   using that CLI.

Setup lives centrally, so future moves (action bump, model, tool scope, CLI version) are a
re-run of migrate-infer.yml instead of a hand-edit per repo.

Ran in CI (mirrors bump-adl.yml):

• sed the inference-gateway/cli pin in .flox/env/manifest.toml to the latest release
• flox upgrade infer + flox activate to refresh .flox/env/manifest.lock
• flox activate -- infer init --overwrite --skip-migrations to regenerate .infer/

Heads-up: infer init --overwrite resets .infer/ to CLI defaults. .infer/agents.yaml
and .infer/mcp.yaml (this repo's A2A agents registry + MCP servers) are preserved
byte-for-byte; every other config file (config.yaml, prompts.yaml, keybindings.yaml,
channels.yaml, computer_use.yaml, heartbeat.yaml, shortcuts/*) is regenerated.
.infer/bin, logs, history and the conversations DB stay out via the nested
.infer/.gitignore. Review the diff before merging.

Notes

• Triggers on @infer mentions in issues / issue comments. Default model
  deepseek/deepseek-v4-flash. The infer-action pin lives in the reusable infer.yml.
• Also adds a manual workflow_dispatch form: from this repo's Actions tab pick Infer,
  type a free-text prompt, and the bot works it in that run and opens a PR (no issue
  needed) - mirroring the @claude workflow.
• Tools = infer-action's default bash whitelist + the language preset (+ markdownlint where
  set), configured in repos.yaml (the entry's orchestrators.infer block).
• Requires the @infer GitHub App (INFER_APP_ID / INFER_APP_PRIVATE_KEY) installed on
  this repo plus the provider API-key secrets; both reach the reusable workflow via
  secrets: inherit.

Filed by migrate-infer.yml.