chore: fix data races in logger #2808

Job	Run time
Run tests and lints	6m 59s
Run OIDC conformity tests	17m 56s
Run end-to-end tests (postgres)	4m 37s
Run end-to-end tests (memory, --jwt)	4m 21s
Run end-to-end tests (mysql, --jwt)	4m 27s
Run HSM tests	5m 26s
Run end-to-end tests (cockroach, --jwt)	5m 29s
Run end-to-end tests (postgres, --jwt)	4m 25s
Run end-to-end tests (mysql)	4m 25s
Run end-to-end tests (memory)	4m 22s
Run end-to-end tests (cockroach)	5m 26s
Build CLI docs	1m 18s
Generate release	0s
Draft newsletter	-1s
Pending approval Slack notification	-1s
Send newsletter	-1s
	1h 9m 8s

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