I’m not sure about where you live but where I live (Canada) you can’t legally do your own heat pump installations. You need to be certified to handle refrigerants and that sort of thing.
I'm from the UK. I was under the impression you could do it yourself here but couldn't find a definitive answer.
It's absolutely something I wouldn't take on myself though. Changing a light switch or rewiring a plug, sure - but I'd be guaranteed to make a huge, expensive, inefficient mess with a project like that.
Yes, for example a mini split unit. You can purchase these at the hardware store and install them yourself. You just can’t do this with units that integrate into a central heating/cooling system which require the installation and charging of the refrigerant lines.
Just in case you don't know it, you may be interested in the videos about heat pumps, and other related technologies on 'Just Have a Think' channel https://www.youtube.com/@JustHaveaThink
https://youtu.be/7J52mDjZzto https://youtu.be/MFEHFsO-XSI https://youtu.be/7zrx-b2sLUs https://youtu.be/43XKfuptnik