Is it common to change the type of engine during major overhauls?
Not common but not unheard of. Overhauls are the major avenue by which older aircraft variants receive upgrades, effectively becoming newer variants (or functionally equivalent to them). Engine upgrades can be one of the easier changes to make, assuming the new engine was designed to be a "drop-in replacement" (mounts and fuel/electrical connections identical, so you just bolt it on possibly with a token change to the housing). Other changes between variants can be much more in-depth, like stretching the fuselage or altering wing length and profile, which are not typically done to aircraft that have already entered service.

In GA, this tends to be more common, as many of the airframes in the GA fleet are decades old (thanks to strict maintenance requirements keeping them serviceable much longer than the expected useful life of a car), and so the benefit of more modern technology of all kinds, including in the engines, tends to justify the costs. Major airlines very rarely do this kind of thing, especially with engines, as jet engines are ridiculously expensive, and when the engine's reached the end of its useful service life, the airframe usually isn't far behind. It's sometimes done to really big, really expensive aircraft like 747s, and the military has done a few "service life extension programs" that involve replacing engines on venerable airframes like B-52s and C-130s.

As far as invalidating ratings, well yes, the original aircraft specs in the POM would no longer apply after an up-engine. The aircraft, as a unit, must be re-rated both theoretically and empirically by an FAA inspector to determine its new specs, and whether all the components of the aircraft can handle them safely (a more powerful engine does not necessarily mean the aircraft can be rated for a higher "do not exceed" speed, if the limiting factor wasn't the engine but the airframe's ability to take the stress). The easiest types of upgrades to get approved are ones that turn the aircraft into a more powerful factory variant of the airframe; for instance, dropping a 235 engine into what used to be a Cherokee 180. With a few other tweaks to bring the entire aircraft up to the specs of a 235, it can be evaluated as if it were one.