Ring view accessed via ingester shows unhealthy ingesters, even if they are healthy

[pstibrany]

Describe the bug

In #654 we have introduced ability to view ingester ring state via endpoint in ingesters. This endpoint however uses "heartbeat period" for "heartbeat timeout" when rendering the page, which is a bug. Hearbeat period is often much shorter (eg. it defaults to 5s for -ingester.ring.heartbeat-period flag) than heartbeat timeout (-ingester.ring.heartbeat-timeout defaults to 1min), so ingesters show up as "Unhealthy", even if they are not.

Link to the code: https://github.com/grafana/dskit/blob/25baa36b7a6fca2025c4e15d7e95d4810c85fa16/ring/http.go#L109

Notice how lifecycler passes HeartbeatPeriod to the ring handler, while "ring.go" used by distributor passes correct HeartbeatTimeout:

To Reproduce

1. Start Mimir (SHA or version)
2. Access /ingester/ring endpoint on ingesters, notice unhealthy ingesters.
3. Access /ingester/ring endpoint on distributors, ingesters will look healthy there.

Expected behavior

Ring page should show the same information when accessed via distributors and ingesters. In particular, ingesters should not use "heartbeat period" instead of "heartbeat timeout".

Additional Context

Original public Slack thread: https://grafana.slack.com/archives/C039863E8P7/p1653301187771079