Investigate prebuild create vs claim build times in dogfood

## Description

In our dogfood environment, the “Write Coder on Coder” template has prebuilds enabled for certain presets. We recently introduced new metrics for prebuild creation time (building into the pool) and prebuild claim time https://github.com/coder/coder/pull/19503, and added them to our observability stack.

These metrics show that claim durations sometimes exceed creation by about 1–2 seconds. Because prebuilds maintain a ready-to-use pool to reduce workspace start time, claims should be consistently faster than creations.

We already use a Terraform `lifecycle` block with `ignore_changes` as recommended in the [docs](https://coder.com/docs/admin/templates/extending-templates/prebuilt-workspaces#preventing-resource-replacement), yet this pattern suggests Terraform may still be replacing or re-provisioning resources during claim, or the claim path is performing extra work.

For reference, see the attached screenshot comparing average build times for a prebuild creation versus a claim on the Falkenstein preset in our dogfood instance.

## Investigation scope

Investigate the source of the additional claim-path latency relative to the create path.

Start with the prebuild creation and claim metrics in the observability stack, comparing the Falkenstein dogfood data and the Terraform lifecycle block with ignore_changes described in the linked documentation. Trace the create and claim paths to identify the source of the extra 1–2 seconds; done means the additional claim latency is explained and any Terraform replacement or reprovisioning is confirmed or ruled out.

Written by the indexing model from the issue text.