major fixes + performance improvements

[sawyershoemaker]

fixes stale hints, clipped overlays, and stalled connections while cutting repeated solver, capture, and rendering work.

• expanded exact solving with grouped cells and compact mine-count distributions; preserved logical certainty for very small probabilities
• added revision-checked solver jobs, atomic deltas, and no-op handling so geometry changes keep valid work and old results cannot repaint a newer board
• made painting incremental, clipped marks to their cells, and added page overflow/native window clipping, including window cutouts
• improved capture scheduling, tab/document lifecycle handling, and fresh clipping checks across cell/content changes
• fixed shutdown wakeups, message-loop starvation, socket replacement/write deadlines, and startup cleanup when shortcuts are unavailable

checks:

• GitHub Actions passes on Windows and Linux, including the browser and portable sanitizer checks
• all 6 Windows suites pass in Release and AddressSanitizer, including 66 extension tests and 14 live TCP tests
• full unpacked-extension/native-server Chromium smoke passes
• independent solver audit: 1,239 cases, 457,186 probability comparisons, no false certainty
• local Release benchmarks: about 2.1x faster on 300 expert snapshots and 5.3x on the connected-frontier workload; software raster updates improved substantially. These are specific workloads, not live-game latency guarantees.

remaining limits: ordinary unclipped boards still assume regular interior cells; arbitrary CSS/animation effects and visual occlusion are not fully covered. Maximum-size clipped boards can be expensive. Mouse safety checks where a left-button press starts; drag releases and alternate input modes remain outside that protection. Mixed-monitor DPI and live OBS/Discord capture still need manual validation.