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.
Buy one that has precharged refrigerant in the condenser. New units use R410a which does not deplete ozone. You'll also never need to handle refrigerant, only open a valve which release it into the copper lineset.
You can buy a Mr Cool unit, you won't need to cut/flare/vacuum the lineset, just connect. I don't personally don't use them as their units generally cost a bit more, (30$ ~ 50%) and you're stuck with whatever lineset lengths they offer. However it's a great starter install and work just fine.
Cooper-Hunter units come precharged, so fairly easy to DIY.
I was looking at Mitsubishi units, which I believe also come pre-charged. I don't know if it's a local law or if the supplier just didn't want to deal with someone not in the trade.
Do you feel like the number of invisible footguns was manageable? That's always my concern with diy trades stuff, the things that seem fine at install but come back to bite you 6mo later.
In general with contractors, you aren't paying for them to do the simple stuff right. You're paying them to get the one or two weird bits of the job done quickly and efficiently because they've seen something like it before and have the tools and parts on their truck.
That is why I didn't try to DIY. Sure I'm confident I could get it installed. However I'm sure that I would discover after the old furnace was tore out that I'm missing some part/tool and so off to the store - what would take a pro a single day would take me 3 weekends at best: time that I don't have HVAC.
There's a bunch of DIY heat pump install videos on YouTube, I watched this one recently: https://www.youtube.com/watch?v=79C2StyNlBg Honestly it convinced me that it's beyond my skillset.
No invisible footguns, just a bit of anxiety releasing refrigerant and hoping my lineset connections don't leak. Theres only a preset amount of refrigerant, it dissipates into the air and theres no easy way to refill it.
That said, some will inevitably leak out (ie. while disconnecting manifold gauge set) but no big deal. I've done four installs and nothing catastrophic.
It costs about 2kUSD to get air to air exchange heatpump installed here (minisplit, includes the cost of the pump, EU). Takes approx 3 hours.