This reminds me of another annoyance I have. We have a wall mounted thermostat using batteries at the cabin. It controls how much water is let through from the central heating to the floors by sending some radio signal. I would like to be able to control this remotely, for instance to turn on heating a day before arrival. But the only way to do this is to buy a new unit connected to the pipes as well and upgrade the whole thing, which was quoted like $2k++ and need their app and their subscription. But why can't something just mimic the radio signals? That already works today! Why do I have to rebuild the whole heating setup for this? So stupid when technology locks you in without need.
I'm tempted to have a remote controlled screw driver that can twist the knob remotely or something.
There are often controllers which do indeed just mimic the signals. Doesn't work with every appliance, it depends on the way it's implement and if the manufacturer wanted to make that approach infeasible.
But there absolutely are options to record such Signals and then replicate them via home assistant - I used them before to control a ceiling fan and various infrared devices (same idea, but not a radio there instead a "blaster" - I think it was called)
I didn't set it up again after my last move though, as I couldn't mount the ceiling fan in this apartment and the Infrared devices were just my media center (tv, audio), which are hardly in use currently
Take a look at SwitchBot. They have a device that can tap buttons to solve these kinds of problems. They also have a device for tilting blinds by twisting the rod, which could maybe be modified to twist a knob.
I like your approach, it's one I try to use at work as well. Not every problem is a tech problem, many things can be fixed by just talking to humans or changing the process.
In my case the cabin is actually in the town where I grew up, and used as a way to be closer to home and family without overstaying my welcome and also be a bit more free when here (heh). So I do have family that now helps with this, it was mostly in a "can I pay a little not inconvenience them". I arrived here sunday with the heat on and some easter eggs and bunnies on the table put there by my mother, so it's not all bad. :)
I'm tempted to have a remote controlled screw driver that can twist the knob remotely or something.