I am considering a Roborock or a Neato mainly. Does it matter when it comes to HA? What is the use of integration with HA anyway, anything more than just starting and stopping the thing?
Yes, not every vacuum robot will be able to integrate with HA. You have to check this in docs.
Other action than start/stop is for example report the accessories status, like when to change the brush or clean sensor. Some models also gives us the possibility to clean predefined certain areas only by simple choose and click interface.
There are lots of use cases which are not covered by the apps of the vacuums, e.g. I start the vacuum every other day but only if no one is home, if someone is home it is postponed to the next day. Or when someone arrives home the vacuum stops and returns to the base. Or when the vacuum starts I disable my motion sensor so that it doesn’t trigger the alarm. etc. etc.