Please add an example how to format messages, that they will contain timestamp.
The only thing the format string gives you is the ability to specify % in a location and supply the content to print in that location via the optional expression list. If you want to print a timestamp you would need to set it up yourself, probably using to_char(timestamp) as an expression.
Ideally through global/session configuration format for raise messages.
That isn't a thing in PostgreSQL.
You can set up a log file line format that includes such things, but the raw message content for RAISED is no more or less than what you either type literally or it computes from format+expressions.
