Explore possible regression in local simulation performance

[ihincks]

Describe the bug

A user has noticed a dramatic slowdown in SamplerV2 with FakeSherbrooke:

A demo of ~150 4-qubit circuits has gone from taking a few seconds to over 3 minutes on their machine. Switching to 5-qubit FakeManila speeds this back up.

Multi-threading things taking a long time in a quick timing profile. Transpiler or aer related?

Steps to reproduce

@caleb-johnson may be able to produce one. Otherwise, try something as above.

Expected behavior

Small circuits on a large device are just as fast as those same circuits on a small device.