Move adults into empty beds when that shortens the total walk

[kramsey458]

What changes

A pass used to swap adults only between beds adults already occupied, so an empty home beside a workplace was never used (e.g. an empty Mini Lodge next to a Lumberjack Flag whose worker lives across the map). Now each district is solved over its occupied and empty beds, so a worker moves into the empty lodge when that shortens the colony's total walk.

• Solver: Hungarian.Step takes n rows by m ≥ n columns (O(n²m)). A district's columns are its adults' beds, then its empty beds (at most one per adult in each home). The solve budget is n²m/8.
• Snapshot: HomeFree per home. Homes now include every usable home with an empty bed in a district with adults. Children count against beds, so they keep theirs.
• Apply: Cycles.SplitChains splits moves into cycles (head counts kept) and chains (the last move takes an empty bed). Each can be applied on its own. ApplyCycle's existing capacity check turns a chain away as stale if the game filled that bed meanwhile.
• Breeding rule: a chain is turned down (counted as rejected) if it would leave the colony fewer homes that can breed, meaning at least two adults and an empty bed. Counts carry across the chains a pass applies, so the colony's number of breeding homes never falls. A 1-bed lodge can never breed, so filling one costs nothing. Moving out of a two-adult home with a spare bed is refused. The solver itself doesn't know the rule, so a refused chain is proposed again the next day until the colony changes.
• Adapter: Capture lists empty-bed homes through district.GetComponent<DistrictBuildingRegistry>().GetEnabledBuildingsInstant<Dwelling>(), with the same UsableHome and district checks as before.
• A lone adult is no longer skipped.
• PassState version 6: a pass running in an older save starts over once, and remembered route costs carry over.

Not done here

• Not compiled against the game. There are no game DLLs in CI or in this environment. The DistrictBuildingRegistry / GetEnabledBuildingsInstant<Dwelling>() call is unverified. Build locally and run the compiled-adapter check before release.
• The breeding rule ("two adults and an empty bed") is the one the FAQ's replay used. It hasn't been checked against the game's reproduction code.
• Website, README player text and PRODUCT.md unchanged. They describe the released 1.1.1, and merging publishes the site. The FAQ #vacant and #breeding, the index rules, the compare table ("Adults per home"), the #how steps, troubleshooting "Empty beds aren't used" and the "41 automated checks" status line all need updating with the release. The README has an Unreleased changelog entry.

Tests

dotnet run --project OptimizedLocalHousing.Tests -c Release → 45 checks passed. That is the 40 existing checks plus:

• chain/cycle splitting of moves into empty beds, each unit applicable alone;
• the brute-force optimum on 100 small random colonies with empty beds (exact unless the breeding rule rejected a chain), never overfilling a home;
• the empty-lodge-beside-the-workplace case (a paused nearer home is never used; a second pass changes nothing);
• the breeding rule: moving out of a breeding home, or filling a breeding home's last bed, is refused; a move that keeps or makes a breeding home is allowed;
• 60 colonies with empty beds over several passes: head counts change in all 60, and breeding homes never fall;
• empty beds added to the lockstep and save/reload-at-every-tick tests.

CLAUDE.md now expects 45 checks passed.

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