perf(ui): adapt search debounce to runtime latency

[saurabhhhcodes]

Closes #64

Summary

• track active search start time and store the last completed search duration
• maintain effective_debounce_ms with the configured search_debounce_ms as the floor
• raise the effective debounce by 50ms after slow searches and decay it toward the configured floor after fast searches
• reset stale active search timing when switching tabs or clearing search input
• add focused unit tests for slow, fast, capped, and floor-backed debounce behavior

Validation

• cargo fmt --all -- --check
• cargo test
• cargo clippy --workspace --all-targets --all-features -- -D warnings -A dead_code -A clippy::type_complexity
• git diff --check

[vercel]

Someone is attempting to deploy a commit to the pie's projects Team on Vercel.

A member of the Team first needs to authorize it.

[saurabhhhcodes]

CI is green for the repo-owned checks:

• Verify
• Build

Local validation:

• cargo fmt --all -- --check
• cargo test
• cargo clippy --workspace --all-targets --all-features -- -D warnings -A dead_code -A clippy::type_complexity
• git diff --check

The remaining red status is Vercel authorization for the org/team, not a Rust build/test failure.

Could you please review and add scoring labels if this looks good?

Suggested labels: gssoc:approved, level:intermediate, type:performance.