Alertmanager goroutine leak test flakes

[seizethedave]

Describe the bug

I encountered a test flake in CI unrelated to my PR.
Here's the CI job.

--- FAIL: TestDistributor_DistributeRequest (21.47s)
    leak.go:14: found unexpected goroutines:
        [Goroutine 427 in state chan receive, with github.com/oklog/run.(*Group).Run on top of the stack:
        github.com/oklog/run.(*Group).Run(0xc00095cf10)
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:43 +0x251
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).Run(0xc0009de850)
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:108 +0x505
        created by github.com/grafana/mimir/pkg/alertmanager.(*Alertmanager).ApplyConfig in goroutine 217
        	/__w/mimir/mimir/pkg/alertmanager/alertmanager.go:544 +0x228b
         Goroutine 353 in state select, with github.com/prometheus/alertmanager/inhibit.(*Inhibitor).run on top of the stack:
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).run(0xc0009de850, {0x2cb9b58, 0xc001197900})
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:[65](https://github.com/grafana/mimir/actions/runs/11733801665/job/32688750912#step:8:66) +0x1d9
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).Run.func1()
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:102 +0x47
        github.com/oklog/run.(*Group).Run.func1({0xc0004e5340?, 0xc00119f1e0?})
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:38 +0x3a
        created by github.com/oklog/run.(*Group).Run in goroutine 427
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:37 +0xa5
        ]
--- FAIL: TestMultitenantAlertmanager_loadAndSyncConfigs (0.94s)
    leak.go:14: found unexpected goroutines:
        [Goroutine 427 in state chan receive, with github.com/oklog/run.(*Group).Run on top of the stack:
        github.com/oklog/run.(*Group).Run(0xc00095cf10)
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:43 +0x251
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).Run(0xc0009de850)
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:108 +0x505
        created by github.com/grafana/mimir/pkg/alertmanager.(*Alertmanager).ApplyConfig in goroutine 217
        	/__w/mimir/mimir/pkg/alertmanager/alertmanager.go:544 +0x228b
         Goroutine 353 in state select, with github.com/prometheus/alertmanager/inhibit.(*Inhibitor).run on top of the stack:
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).run(0xc0009de850, {0x2cb9b58, 0xc00119[79](https://github.com/grafana/mimir/actions/runs/11733801665/job/32688750912#step:8:80)00})
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:65 +0x1d9
        github.com/prometheus/alertmanager/inhibit.(*Inhibitor).Run.func1()
        	/__w/mimir/mimir/vendor/github.com/prometheus/alertmanager/inhibit/inhibit.go:102 +0x47
        github.com/oklog/run.(*Group).Run.func1({0xc0004e5340?, 0xc00119f1e0?})
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:38 +0x3a
        created by github.com/oklog/run.(*Group).Run in goroutine 427
        	/__w/mimir/mimir/vendor/github.com/oklog/run/group.go:37 +0xa5
        ]

Environment

• GitHub actions.