API to request the timestamp for given LSN

[arpad-m]

On slack, @xenomote has asked for an API for the pageserver to obtain the timestamp corresponding to a given LSN.

For the use case, they write:

when a branch is created by LSN instead of timestamp we currently have no relevant timestamp available to display

The slack thread discusses either returning always also the timestamp in addition to the lsn, say for when we return TimelineInfo from /v1/tenant/{tenant_id}/timeline, or alternatively providing an endpoint like /v1/tenant/{tenant_id}/timeline/{timeline_id}/get_lsn_by_timestamp, just the other way around.

@jcsp has pointed out that computing the timestamp might be non trivial and has suggested the following:

just providing an on-demand API to get timestamp at the start_lsn of a timeline seems like the least-effort way forward.

[arpad-m]

I had a look at the code. It should be pretty easy to traverse the timestamps corresponding to the LSN and then returning the minimum and maximum from the range. We can also run other methods on it, like determining the mean, average, etc. I want to file a PR by the end of the week.