perf(planning): update plan observations incrementally

Cache an immutable occupancy per placements map and derive a candidate's
time-off period groups, holiday-week completeness and placement tie key
from its parent when one date is added or removed. The from-scratch
computation stays as the test oracle and an opt-in shadow mode. A
fast-check property test compares both after every operation.

The loaded year drops from 66.5 s to 48.5 s and the protocol from 262.0 s
to 193.7 s. Outcomes, explanations and final states stay identical.

Refs #283

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

package.json

@@ -64,6 +64,7 @@
 		"eslint": "^10.4.1",
 		"eslint-config-prettier": "^10.1.8",
 		"eslint-plugin-prettier": "^5.5.6",
+		"fast-check": "4.10.2",
 		"jest": "^30.4.2",
 		"jest-preset-angular": "^17.0.0",
 		"jsdom": "^30.0.0",