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Heat pumps can't take the cold? Nordics debunk the myth
(techxplore.com)
This is a most excellent place for technology news and articles.
My quote from the installers that were on the list of qualified installers for the rebate was always around 20K and up for a 3 head system. It was not worth paying the premium to get the rebate but I'm pretty handy on the tools.
I could break my system completely 2 times and still come out spending less when I bought a 3rd one compared to having a "Qualified Pro" install it for me. Especially since I now have all the hole saws, vacuum pump, flare kit, electrical is done etc, so there is no added expense beyond buying the unit now.
If you are not comfortable with gas fittings, electrical, cutting holes in the side of your house etc... It might be a different calculation.
The one I bought is under 4k CAD. https://senville.ca/36000-btu-tri-zone-mini-split-air-conditioner-sena-36hf-t/ and is medium DIY friendly.
You can get brands like Mr.Cool that are very simple to install.