## Summary
Creatures (pets following, monsters chasing, NPCs approaching) would **oscillate — "pace back and forth really fast"** at concave obstacles (reported at the Britain Inn L-desk: a pet at `(1493,1614,20)` never reaching its master at `(1494,1605,21)`) instead of routing around them.
**Root cause** (the A* pathfinder itself was correct): all goal-seeking funnels through `MoveTo` and `WalkMobileRange` → `MoveTowardsOrAwayFrom`, which step greedily via `DoMove(dir, badStateOk:true)`. `DoMove` returns `true` even when the direct step was blocked and the creature merely **auto-turned and sidestepped** (`MoveResult.SuccessAutoTurn`), and the caller then set `Path = null`, discarding the `PathFollower`. So at a concave obstacle a non-progressing sidestep was mistaken for progress and the creature never committed to a route. (AOS pet-follow runs at `CurrentSpeed = 0.1`, hence the "really fast" shuffle.)
## What changed
- **New centralized `BaseAI.ApproachTarget(target, run, range)` primitive.** A greedy step is committed only when it **fully succeeds (`MoveResult.Success`) and actually gets closer**; otherwise the creature commits to a **persistent `PathFollower`** that routes around the obstacle and is never discarded by a greedy step. The open-terrain fast path (one greedy step, no pathfinding) is preserved. `MoveTo`, `MoveTowardsOrAwayFrom`, and `MoveToWithCollisionAvoidance` all delegate to it — public signatures unchanged, so no AI-class call site changes.
- **Best-distance give-up + idle.** A creature that cannot reach a **stationary** in-range goal stops shuffling and idles after `ApproachGiveUpTicks` (40) ticks without lowering its closest-ever distance; a **moving** goal (active chase) never gives up. It resumes the moment the goal moves.
- **Pathfinder fix (required):** `BitmapAStarAlgorithm.IsBlockedByDynamic` now skips the dynamic mobile-block check **at the goal cell only** (`MoveImpl.Goal`). Previously A* returned `null` whenever the target mobile stood on the goal cell, so creatures could never pathfind *toward* another mobile — only toward empty ground. The follower stops within `range` short of it. Static/item blocking and all non-goal mobile blocking are unchanged.
## Tests
New AI-loop integration tests in `ApproachTargetTests.cs` drive the real `BaseAI` primitives against live Britain Inn map statics: exact-repro pet follow, open-terrain (asserts zero pathfinding), `MoveTo` chase (static + walking-away target), route-around-a-dynamic-wall, and walled-off give-up-and-idle.
- Pathfinding + AI subset: **52/52** pass.
- Full `UOContent.Tests`: **301/301** pass. (Note: the test host lingers on shutdown — a pre-existing infra quirk unrelated to this change; all tests complete and pass.)
- Full solution build: clean (0 warnings / 0 errors).
## Notes
- Branched off `main`; independent of the in-flight step-cache work.
- Out of scope (future work): proactive "SmartAI" look-ahead pathfinding so clever creatures plan a route before walking into the obstacle, rather than reacting after they hit it.
## Test Plan
- [X] In-game: order a pet to `follow`/`come` across the Britain Inn L-desk; confirm it routes around and reaches you instead of pacing.
- [X] Aggro a monster and kite it around a building/treeline; confirm it chases around obstacles.
- [X] Confirm open-terrain following/chasing feels unchanged (no extra latency).
- [X] Confirm a creature with a genuinely unreachable target idles rather than shuffling forever.
## Summary
Replaces `FastAStarAlgorithm` with `BitmapAStarAlgorithm`: one cache lookup per cell expansion (8-direction mask + per-direction destination Z) instead of 8 separate `MovementImpl.CheckMovement` calls. Adds the supporting cache infrastructure to back it.
Public API unchanged — `MovementPath` / `Mobile.Move` / `CalcMoves.Find` return the same shapes; the algorithm swap is internal.
## What's in this PR
- **`BitmapAStarAlgorithm`** — A* that issues one `StepCache.TryGetMask` call per cell expansion. Inline fallthrough to the per-cell slow path for multi-Z, off-map, source-Z mismatch, and non-default walkers.
- **`StepCache`** — singleton chunk store keyed by `(mapId, chunkX, chunkY)`. Lazily built on first query, invalidated by `Sector.MultisVersion` mismatch, memory-bounded by sampled probabilistic LRU.
- **`StepProbe`** — computes static-only walkability for a single cell, mirroring `MovementImpl.Check` minus the item / mobile collision phases.
- **`StepMask` / `StepChunk`** — value / storage types for the per-cell results.
- **`CacheEvictionTimer`** — periodic cap backstop (60s interval; early-returns when not over cap).
- **`Map.Sector.MultisVersion`** promoted to `public` so the cache can detect dynamic-static invalidations cheaply.
## Eviction strategy
Sampled probabilistic LRU (Redis-style). Per eviction, sample 5 random keys from a parallel `List<long>` kept in lockstep with the chunk dictionary; evict the oldest of the sample via swap-and-pop. O(1) per eviction regardless of resident count, so sustained cap pressure has no perpetual perf hit.
## Capability handling (interim)
Non-default walkers (non-GM players, creatures with `CanSwim` / `CanFly` / `CanOpenDoors` / `CanMoveOverObstacles`) route entirely through the per-cell slow path via `BitmapAStarAlgorithm.GetSuccessorsSlowPath`. The 2-pass design (cache + capability overlay + dynamic-obstacle pass) lands in the follow-up PR.
