feat(config): user-tunable context window with log-scale slider

[quiet-node]

Summary

• Adds a user-tunable num_ctx setting with a log-scale slider (2K → 1M) and an editable token chip in the AI tab. Slider thumb visually aligns with tick labels at every doubling, and the value chip reflects the exact selected token count.
• Plumbs the configured num_ctx through the /search pipeline so the router and universal judge calls send the same value the chat path and warmup use. Previously these calls omitted num_ctx, causing Ollama to reload the model at its default 4096-token window after the first /search message even when a larger context was configured.
• Folds in the Keep-Warm work this branch was already carrying (pre-load on activation, configurable inactivity timeout, indefinite mode, manual unload, loaded-model status row) since both features touch the same [inference] config section and warmup path.

Context window slider details

• 10 tick labels at every doubling (2K, 4K, 8K, 16K, 32K, 64K, 128K, 256K, 512K, 1M) match the log scale, where each 1/9 of slider travel doubles the value.
• Ticks are absolutely positioned at i / 9 * 100% with an 8px horizontal margin matching the slider thumb radius, so each label sits under the thumb center at that value.
• Fill gradient ends at the thumb center via calc(8px + var(--fill) * (100% - 16px) / 100%) instead of at --fill% of full track width.
• Editable token chip accepts any value >= 2048; out-of-range values fall back to the previous valid value on blur.

Search-path num_ctx fix

• RouterOptions carries num_ctx; request_json, call_router_merged, and call_judge accept it as an argument.
• DefaultRouterJudge and DefaultJudge carry num_ctx, populated from app_config.inference.num_ctx in search/mod.rs.
• Two new wire-level tests assert the request body contains "num_ctx":<value> for both router and judge calls.

Test plan

• bun run test:all:coverage — 1152 vitest tests + 670 cargo tests pass with 100% line coverage gate
• bun run validate-build — lint + format + typecheck + frontend + backend release bundle clean
• Manually verify slider thumb position matches the value chip across the full range (2K → 1M)
• Manually verify /api/ps reports the user's configured num_ctx after the first /search message (no auto-reset to 4096)
• Manually verify Keep Warm: pre-load on activation, custom inactivity timeout, indefinite mode (-1), and the Unload now button