[nextest-runner] use TestInstanceId in more spots #5382

Job	Run time
Test archives with a target runner	1m 53s
Build documentation (ubuntu-latest)	1m 23s
Build and test (ubuntu-latest, 1.81)	5m 35s
Lint (ubuntu-latest)	44s
Build and test (ubuntu-latest, stable)	3m 51s
Lint (windows-latest)	2m 10s
Build and test (macos-14, 1.81)	5m 21s
Build and test (macos-14, stable)	4m 9s
Build and test (windows-latest, 1.81)	8m 11s
Build and test (windows-latest, stable)	7m 0s
Test archives with a runner (destination) (ubuntu-24.04, ubuntu-latest)	11s
Test archives with a runner (destination) (windows-latest, windows-latest)	26s
	40m 54s

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