I would really like to be able to pass the WMS request with a local timezone rather than converting all the time between UTC and local time. I misinterpreted the documentation as I thought I could simply append my local timezone, but it seems this is not supported. Are there plans to support local timezones?

From the documentation:

The time range for which to return the results. The result is based on all scenes between the specified times conforming to the cloud coverage criteria and stacked based on priority setting - e.g. most recent on top. It is written as two time values in ISO8601 format separated by a slash, for example: TIME=2016-01-01T09:02:44Z/2016-02-01T11:00:00Z . Reduced accuracy times, where parts of the time string are omitted, are also supported. For example, TIME=2016-07-15/2016-07-15 will be interpreted as “TIME=2016-07-15T00:00:00Z/2016-07-15T23:59:59Z” and TIME=2016-07/2016-08 will be interpreted as “TIME=2016-07-01T00:00:00Z/2016-08-31T23:59:59Z”

Passing the local timezone seems to work, but in reality, it just returned me the most recent image no matter what dates I give it. It would be better to throw an error saying something like “timezone is not supported”.
time: 2023-06-25T13:00:00+10:00/2023-06-25T20:00:00+10:00/P1D

This works, but UTC time is assumed:
time: 2023-06-25T13:00:00/2023-06-25T20:00:00/P1D