You don't say this, but I presume you have the microwave plugged into a 20a
kitchen circuit that complies with code by being protected by a GFCI.
Is that correct?

When you plug your tester in, the test button trips the GFCI instantly and
allows immediate reset.
When the microwave trips the GFCI, it takes an hour before you can reset.
Is that correct?

Do you leave the microwave plugged in for that hour, or do you unplug it?
If you leave it in, perhaps the microwave takes that long to resolve it's
fault. If you unplug it, you must have a defective GFCI.

There are 15a and 20a GFCI outlets, but afaik they are the same except for
the prong configuration.