Ask your realtor for references.
There is, unfortunately, no shortcut to finding quality handymen.
Instead they act as an information hub for homeowners.
Obviously "good realtor" is doing a lot of work here, and I don't know how you find a good realtor (kind of lucked into mine after having a terrible one for my first purchase).
She would get recommendations from sellers. Either the seller recently had work done in order to improve the home before putting it on the market, or, the seller had some trusted expert they used for years.
My realtor actually encouraged me to ask her for any contacts if I needed something done in the future. I sense that her contacts like having customer referrals as well.