I use a Broadlink RM Pro with Home Assistant to control my older Daikin heat pump. I'm using it as a dumb IR blaster, and you would be better off with a newer non-pro model I think, possibly from Ali Express. If no-one else has already done it for your make model of heat pump you have to record the codes you want to send which is a little tedious, but not difficult or too time consuming (integration, discussion). Near the end of the discussion is instructions how to do it, if you need help send me a message. If you want to use the Broadlink app it has a database of many heat pumps that works quite easily, but I prefer Home Assistant.
I have a hardware gateway for my roman blinds that I got from the place that sold the blinds to me. Their app / Home Assistant talk to the gateway, which talks to the blinds using RF. I use "Motion Blinds Gateway", which I think is this integration. I don't have the brands that it says to use, but it seems to work fine.
Button as an automation trigger... I haven't done that yet. I do have some Athom ESPHome smart plugs that integrated into Home Assistant with zero effort. If you look at "Wall Switches For ESPHome" on that page maybe they'll work, but it looks like they need to be wired in, which is different from what I think you want. I'd be interested if you find anything.
I have an Android tablet on the wall that runs my ducted heating system, Airtouch, and I've installed the Home Assistant app on. It's pretty easy to make a dashboard with buttons / sliders / etc to control what you want with that. When I say easy, Home Assistant has a bit of a learning curve, but I've only been using it for maybe six months and I can do most things I need to, sometimes with a bit of community help. The HA community is pretty good.