It is not a requirement to vent your OTR microwave out of the home but it is a good idea to do so for a number of reasons
Replacing a Range Hood with a Microwave
Why You Should Avoid Over-the-Range Microwaves - Today's Homeowner
Install an over-the-range microwave oven
Do Range Hoods Have to be Vented Outside? - THOR Kitchen
Range Hood vs. Over the Range Microwave Comparison
What to Do if Your Range Vent Hood Leaks Cold Air - This Old House
How to Install an Over-the-Range Microwave to Save Kitchen Space
What To Do If You Don't Have a Range Hood or Vent
Pros and Cons of Over-the-Range Microwaves
Over the range microwave blowing air from the top : r/Appliances
Should You Vent an Over-the-Range Microwave Outside?