analytical-viz: add sidebar Batch B selectbox + wire through all suggesters

New sidebar widget in the Workload expander:
  Batch B (concurrent requests) — selectbox 1/2/4/…/256, default 1.

Wired end-to-end:
  - app.py sidebar → forwards b_batch when constructing the main topo
  - auto_suggest(..., b=1) — passes b to _score_candidate, which builds
    TopologyConfig with b=b
  - run_auto_explore(..., b=1) — sets topo.b = b for every enumerated
    candidate before scoring
  - joint_explore(..., b=1) — forwards b to _best_parallelism_for_hw
    and _best_parallelism_two_stage; both set topo.b = b before scoring

All button handlers (sidebar Apply-scope, Physical Layout scope,
Auto Suggest tab sweep, Auto Hardware tab sweep) now pass b_batch.

Combined with the earlier partial-scaffold commits (memory_layout
scales KV by B; stage_rmsnorm / stage_wq / stage_wkv / stage_kv_append /
_per_hop_qkT_pv scale flops + activation memory by B), changing B in
the sidebar now affects reported latency and per-PE memory footprint
in the visible parts of the pipeline. The remaining FFN + comm-AR
stages still ignore B (they'll be next); their contribution is small
for the memory-bound decode case that matters most, but latency for
FFN-heavy configs at high B will be slightly under-reported until
those are scaled too.

Verified: 24 pytest tests pass at default B=1 (backward compat).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

tests/analytical_visualization/auto_hardware.py

@@ -237,6 +237,7 @@ def _best_parallelism_for_hw(
     model: ModelConfig, machine: MachineParams,
     s_kv: int, mode: str,
     include_attention: bool = True, include_ffn: bool = True,
+    b: int = 1,
 ) -> ConfigScore | None:
     """Return the latency-minimum feasible parallelism for this HW.
 
@@ -247,6 +248,7 @@ def _best_parallelism_for_hw(
     best: ConfigScore | None = None
     best_key: tuple | None = None
     for topo in _iter_reduced_parallelism(model, s_kv, mode):
+        topo.b = b
         cfg = FullConfig(model=model, topo=topo, machine=machine)
         s = score_config(cfg, include_attention=include_attention,
                           include_ffn=include_ffn)
@@ -265,13 +267,14 @@ def _best_parallelism_two_stage(
     model: ModelConfig, machine: MachineParams,
     s_kv: int, mode: str,
     include_attention: bool = True, include_ffn: bool = True,
+    b: int = 1,
 ) -> ConfigScore | None:
     """Fast fallback: use autosuggest's memory-min (CP,TP,PP) then score it."""
     sug = auto_suggest(model, machine, s_kv, mode)
     if not sug.fits:
         return None
     topo = TopologyConfig(
-        cp=sug.cp, tp=sug.tp, pp=sug.pp, dp=1,
+        cp=sug.cp, tp=sug.tp, pp=sug.pp, dp=1, b=b,
         s_kv=s_kv, mode=mode,
         kv_shard_mode="split",
         ffn_shard_scope="TP+CP",
@@ -366,6 +369,7 @@ def joint_explore(
     depth: str = "balanced",
     include_attention: bool = True,
     include_ffn: bool = True,
+    b: int = 1,
 ) -> JointExploreResult:
     """Sweep HW candidates × parallelism, return joint Pareto + sensitivity.
 
@@ -383,11 +387,13 @@ def joint_explore(
             par = _best_parallelism_two_stage(
                 model, machine, s_kv, mode,
                 include_attention=include_attention, include_ffn=include_ffn,
+                b=b,
             )
         else:
             par = _best_parallelism_for_hw(
                 model, machine, s_kv, mode,
                 include_attention=include_attention, include_ffn=include_ffn,
+                b=b,
             )
         if par is None:
             continue