Is your feature request related to a problem? Please describe.
When analysing historic cluster behaviour using metrics dashboard on web ui it is necessary to zoom into particular time range and then progress between dashboards e.g. from slow requests to overload to hardware.

If something goes wrong with chart due to ui bugs you have to reload page to restore the state, but that doesn't preserve the time range. So you have to pick the new range again. This is the first problem.

Then you have to go through date and time pickers which doesn't allow you to type the date/time. And the dialog always starts from current time even if you already have a range picked. Which makes extending the time range painful as well.

Describe the solution you'd like
Preserve displayed time range when page is reloaded.

Allow typing the range and copying its value which may help as a stopgap if we can't preserve it during reload.

Make range picker start from current values.

Describe alternatives you've considered
The alternative is to use external monitoring, but it is not possible in cases where you need to analyse exported time series from on prem client clusters or from roachtest runs.

Additional context
This problem gets very irritating when hitting any bugs in charts that force you to reload page frequently (see #71201)
Time picker is a real pain when debugging clusters behaviour but we don't have any alternative to this.

Epic CC-5280

Jira issue: CRDB-10438