I looked into doing my own heat pump install. At least here in Vermont, you can't buy one without a refrigeration license[0] because of the ozone depletion issues with refrigerants. You
also have to buy one from an in-state supply house to qualify for some of the incentives. Not all supply houses will sell to muggles.
My experience was that it was simpler and quicker to pay someone despite having basically the simplest possible installation: inside and outside units on opposite sides of the same exterior wall. The guy was great, and recommended a unit with an easily removable blower wheel for the dusty wood shop application[1]. I wouldn't have gotten there on my own, for sure. And he made sure that it qualified for the incentives. The list is long, and the models that are actually in production/available change pretty regularly.
Technically, it can be a pretty simple job. Practically, local regulations and circumstances might sway things towards hiring it out.
I say all this as someone who is a fairly competent shade-tree mechanic. I've done an engine swap and replaced a couple of clutches (transmission seal failure and previous owner's poor work; I know how to drive stick)
[0] I'm playing fast and loose with the exact words; it's been a few months since I looked into it.
[1] Cooper-Hunter, which is a Midea brand