The documentation: https://tempoplugin.jira.com/wiki/display/TEMPO/Tempo+dynamic+drop-downs - last heading, implies it can send the issue key.
In which case you should be able to get the url from the servletRequest: https://scriptrunner.adaptavist.com/latest/jira/rest-endpoints.html#_configuration
Then look up the issue, and get the type.
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