This is an interesting project to get a simple motorised garage door opener to connect with some intelligence via Home Assistant.
One could split this into two phases, with the first being really simple and not interfering with the motorisation itself. The first phase could just use the reed switches to indicate on the Home Assistant dashboard whether the door is fully closed, open, or somewhere in between (i.e., jammed or stopped). You could set easy automation rules too to have a timer running when the door opens, and if it is not closed within say 2 minutes, to send an alert to you. Or if the door opens after dark, send an alert to you. The sky is the limit with the rules you can build into Home Assistant to automate things for you.
Getting fancier on phase one, you could add an ultrasonic detector to look downwards and see if the car is in the garage (shorter distance) or it is out (full distance to the floor). The opening / closing automation could take the car’s presence into account as well.
Phase two would have some interface with the motor. But this can be quite simple too, as even my old 15+ year old DC Blue garage opener, as a manual test button on the board. This is for simulating the remote-control button. Some also have a switch on the wall for this purpose. Either ways, you can use the contacts of this button / switch to make or break the circuit to trigger the opening or closing. So, no need to have some super fancy, expensive door opener to get something like this done.
This is also not the only way to do this project, as Home Assistant has a number of project recipes to work with different devices. So, consider others if this looks a bit complex, or consider my phased approach too, to get yourself tempted for phase two.