"target-only" inhibition rules only work if there're other alerts firing

What did you do?

Assume I have a setup where I have "trigger alerts" that are basically only used to inhibit other alerts or I want to inhibit whole categories of (noisy) alerts. I have found "target-only" inhibition rules (i.e. rules with only target_matchers but no source_matchers or equal) to be a great "loop hole" for simple "self-inhibiting" rules:

inhibit_rules:
[...]
- target_matchers: [ severity="notify" ]  # i.e. trigger alerts
- target_matchers:
    - device_role="laptop"
    - severity="warning"
    - alertname=~"HostSwapIsFillingUp|HostOutOfMemory|PrometheusTargetMissing":
[...]

What did you expect to see?

These should inhibit the matched target alerts (since there's no overlap with source_matchers the exception for self-inhibiting rules does not apply).

What did you see instead? Under which circumstances?

These (target-only) inhibition rules worked as expected (not sure if intended or not 😉 ) for 6-8 weeks, but started experiencing "racy" behavior. I couldn't exactly pinpoint when it started, but my observation over the last weeks was:
if there're only alerts firing which should be inhibited by these target-only rules they will not be inhibited. Once a non-inhibited alert fires the target-only inhibition rules are applied again. This is most obvious when there're only one or two alerts in flight.

All other inhibition rules seem to work without problems.

Environment

• System information:

Docker version 20.10.11, build dea9396 on Ubuntu 20.04.3 LTS (GNU/Linux 5.11.0-41-generic x86_64)

• Alertmanager version:

$ docker exec alertmanager alertmanager --version
alertmanager, version 0.23.0 (branch: HEAD, revision: 61046b17771a57cfd4c4a51be370ab930a4d7d54)
  build user:       root@e21a959be8d2
  build date:       20210825-10:48:55
  go version:       go1.16.7
  platform:         linux/amd64

• Prometheus version:

$ docker exec prometheus prometheus --version
prometheus, version 2.31.1 (branch: HEAD, revision: 411021ada9ab41095923b8d2df9365b632fd40c3)
  build user:       root@9419c9c2d4e0
  build date:       20211105-20:35:02
  go version:       go1.17.3
  platform:         linux/amd64

Start by reproducing the reported configuration with only alerts matching target-only inhibition rules, then repeat with one non-inhibited alert present. Trace Alertmanager's inhibition evaluation and add a regression test covering both cases. Done means target alerts are inhibited consistently even when no non-inhibited alert is firing.