feat(multiplayer): add server process/assignment-ready registration API

Add POST /v1/servers/{id}/register (and its /api/v1 contract alias),
authenticated by the same workload binding as the result route. A
game server reports its protocol version and image digest and asks
to advance ALLOCATING -> PROCESS_READY -> ASSIGNMENT_READY; the store
boundary (AdvanceServerRegistration) does this as one idempotent
SERIALIZABLE transaction that also advances every participant's queue
ticket, and gates the final transition on every participant having a
live, unexpired assignment.

Adversarial review of the surrounding routing turned up a pre-existing
bug: contractServerMutation rejected any path containing '/', so the
already-documented /api/v1/servers/{id}/result route (and this new
/register route) 404'd for every real caller despite being declared
in the OpenAPI contract. Fix it to delegate shape validation to
serverMutation, matching how contractQueueMutation handles its own
two-segment paths, and add a regression test covering both contract
routes end to end.

server/api/store_adapters.go

@@ -58,3 +58,16 @@ func ProposalPromoterFromStore(db *sql.DB) ProposalPromoter {
 		return store.PromoteStoredAcceptedProposal(ctx, db, proposal.ProposalID, now)
 	})
 }
+
+type postgresServerRegistrar struct{ db *sql.DB }
+
+func (p postgresServerRegistrar) RegisterServer(ctx context.Context, binding domain.WorkloadBinding, protocol int, assignmentReady bool, idempotencyKey string, now time.Time) error {
+	return store.AdvanceServerRegistration(ctx, p.db, binding, protocol, assignmentReady, idempotencyKey, now)
+}
+
+func ServerRegistrarFromStore(db *sql.DB) ServerRegistrar {
+	if db == nil {
+		return nil
+	}
+	return postgresServerRegistrar{db: db}
+}