Emit breadcrumbs for `genericPoolIntegration`

[timfish]

We should emit breadcrumbs for the genericPoolIntegration.

It is important not to tie this to spans, as these have no data when not sampled. Instead, where possible we need to use hooks in instrumentation to create breadcrumbs.

[timfish]

I clicked "convert to issue" in #13680 but we don't need individual issues.