test failed in CI: Several time outs when starting sled agent during volume management tests

This test failed on a CI run on #9967:

https://github.com/oxidecomputer/omicron/pull/9967/checks?check_run_id=65663757734

Log showing the specific test failure:

https://buildomat.eng.oxide.computer/wg/0/details/01KJV88QZMY7XYDA68M86AQDEN/3Z51mBzelMabtysXy2wkNKxpJLrMa5bziwOcBJEeTYtiS5wB/01KJVJ84KQJ24PEY27HE7CSDPN#S8664

https://buildomat.eng.oxide.computer/wg/0/details/01KJV88QZMY7XYDA68M86AQDEN/3Z51mBzelMabtysXy2wkNKxpJLrMa5bziwOcBJEeTYtiS5wB/01KJVJ84KQJ24PEY27HE7CSDPN#S8788

https://buildomat.eng.oxide.computer/wg/0/details/01KJV88QZMY7XYDA68M86AQDEN/3Z51mBzelMabtysXy2wkNKxpJLrMa5bziwOcBJEeTYtiS5wB/01KJVJ84KQJ24PEY27HE7CSDPN#S8965

https://buildomat.eng.oxide.computer/wg/0/details/01KJV88QZMY7XYDA68M86AQDEN/3Z51mBzelMabtysXy2wkNKxpJLrMa5bziwOcBJEeTYtiS5wB/01KJVJ84KQJ24PEY27HE7CSDPN#S9073

Excerpt from the log showing the failure:

thread 'integration_tests::volume_management::test_upstairs_notify_downstairs_client_stop_request' (2) panicked at nexus/src/lib.rs:490:14:
Could not initialize rack: ServiceUnavailable { internal_message: "Failed to access DB connection: Backends exist, and appear online, but all claims are used" }

thread 'integration_tests::volume_management::test_proper_region_sled_redundancy' (2) panicked at /work/oxidecomputer/omicron/nexus/test-utils/src/resource_helpers.rs:2096:10:
expected to find inventory collection: TimedOut(400.373382994s)

thread 'integration_tests::volume_management::test_upstairs_notify_downstairs_client_stops' (2) panicked at /work/oxidecomputer/omicron/nexus/test-utils/src/starter.rs:241:21:
Timed out after 600s while running step start_sled1

thread 'integration_tests::volume_management::test_upstairs_repair_different_upstairs_retry' (2) panicked at /work/oxidecomputer/omicron/nexus/test-utils/src/starter.rs:241:21:
Timed out after 600s while running step start_sled1

At first I was going to add this to https://github.com/oxidecomputer/omicron/issues/8738 but looking a like deeper it seemed that the error was in the simulated sled agent.

Start with the linked CI run and the four failure excerpts, then read nexus/src/lib.rs, nexus/test-utils/src/resource_helpers.rs, and nexus/test-utils/src/starter.rs at the reported lines. Reproduce the volume-management integration-test failures and trace the simulated sled-agent startup and inventory-collection timeouts. Done means the affected tests complete without the reported initialization or timeout failures.