refactor(gui): group board state flags into typed state objects

[StudentWeis]

Summary

Refactor board and settings state into grouped state objects so the board logic reads in terms of domain state instead of scattered top-level flags.

Linked Issue

Closes #107

Changes

• group board UI and search-related flags into UiState and FilterState
• group settings editor booleans into nested state structs and update dependent call sites
• replace row render booleans with typed render flags for clearer conditional rendering

Testing

• scripts/precheck.sh passes locally
• New / updated tests cover the change
• cargo test --quiet board

Self-Check

• PR title follows Conventional Commits
• No hardcoded user-facing strings — i18n keys added to all locale files
• New UI components use gpui-component
• Errors defined with thiserror (no manual impl Display/Error)
• No unrelated changes mixed in