Stacked on #2594. Fixes jerky creature movement (lich / Fast-bucket melee chases) by choosing the client animation flag from the actual step pace instead of a caller-supplied `run` argument, and fixes three step-pacing defects in the move budget found while verifying it with paired server/client traces.
### Why
The `Direction.Running` bit does nothing for creatures server-side (`Mobile.OnMove` reads it only for the player throttle and stealth reveal). Its whole effect is on the client, which animates each step over a fixed time selected by that bit: walk 400 ms / run 200 ms on foot, 200 / 100 ms mounted. ClassicUO queues up to 5 steps and *drops* the sixth, so a creature stepping every 300 ms while flagged as walking backs the queue up until it snaps forward — the observed jerk.
The `run` argument never carried the one fact that matters (the step interval). RunUO passed `true` in combat / `false` for pets and gated it on `dist > 5`; #2271 flipped every combat site to `false`; pets passed `currentDistance > 2`. None of that is a coherent signal.
### What
**Pace-derived run flag**
- `BaseAI.ShouldRun()`: run iff the effective step delay (move clock + badly-hurt inflation) is shorter than `Movement.WalkFootDelay` / `WalkMountDelay` (mounted or flying) — with a continuity rule: an *isolated* step (taken after standing at least a walk interval) goes out as a walk, because the client renders each step alone and a lone run-flagged step is a 200 ms dart. Only a continuing cadence flags run; a true sprinter (pace under the run interpolation) always runs, since a walk-rendered first step would flood the client's 5-step queue. This reproduces RunUO's close-in feel (its `dist > 5` gate) from first principles.
- `DoMoveImpl` stamps the bit; it is the single place the flag is set.
- `run` removed from `MoveTo`, `WalkMobileRange`, `ApproachTarget`, `MoveToPoint`, `MoveToWithGroup`, `MoveToWithCollisionAvoidance`, the move intent, and `PathFollower.Follow`. All 35 call sites updated. **API change** for custom scripts — documented in the RunUO migration docs (`09-items-mobiles-creatures.md`, `11-api-reference.md`) and `content-patterns.md` § Creature Speeds.
**Move-budget pacing fixes** (each confirmed by UTC-aligned server/client step traces)
- A stall no longer banks catch-up steps: the budget's snap-to-now released up to three steps in ~300 ms when a creature resumed chasing after standing beside its target — rendered as a teleport.
- Debt accrual removed entirely: a step landing sub-period late (think-grid vs budget misalignment during reactive mirroring) kept the remainder and fired a follow-up ~100 ms later — a dart pair. `ConsumeMoveBudget` now paces every step from when it was actually taken; in continuous pursuit the move-wake lands within wheel resolution of the deadline, so the cost is single-digit-ms drift.
- Net effect: a creature can never step faster than its pace, verified across a full chase session (zero sub-pace steps; metronomic 350 ms cadence for a 0.3 s lich).
- Test fixture now runs `Movement.Configure()` (the walk delays were 0 in tests).
### Accepted trade-off
Animal (LOW group) bodies without a run animation slide on their stand frames when flagged as running. Most are slow enough to stay flagged as walking; the client-side fallback is in ClassicUO/ClassicUO#1930.
### Tests
`RunFlagTests`: foot thresholds (0.3 / 0.125 run; 0.4 / 0.45 / 1.05 walk), flying uses the mount threshold, badly-hurt inflation flips a 0.35 s creature back to walk, a real `DoMove` stamps the bit, isolated steps drop to walk (sprinters keep running), a stall restarts the cadence with no banked steps, and a late step earns no quicker follow-up. Full suite: 837 Server + 747 UOContent green.
e07416902a