Any suggestions for a good robot vacuum + mop?

With valetudo you should be able to accomplish what you're looking for. They also have a list of supported vacuums my friend owns the Dreamtech Z10 and highly recommends it. I'm waiting for my current Wyze hand me down to kick the can then I plan on picking it up :)

Consider buying one that is supported by Valetudo. It's so much better to be cloud free.

Not sure about local control, but I've been pleased with the Roborock line.

This is the first I'm hearing of Neato shutting down. They made great products so this is a bummer.

I've heard good things about Valetudo, a custom firmware for vacuums, specifically when paired with Roborock vacuums. The more recent models seem much more of a pain to root though so I decided against replacing my last Neato that broke and was going to see how the market shaped up.

Unfortunately with Neato exiting it seems like things are only going to consolidate more around expensive cloud-heavy models.

Roborock S7 series seems to be the best on the market. Once setup in the Home Assistant integration you can control the vacuum without having an active internet connection. I just tested this by disconnecting my WAN and starting a cleaning.

S7 = Robot vacuum with vibrating mop that lifts up over carpet. Some of the best (if not the best) LIDAR mapping and navigation on the market.
S7 Plus = Same as above with auto empty dock (see below for my personal opinions)
S7 VMax = Same as the S7 but adds AI object avoidance (via front facing camera) for things like shoes, cords, poop, etc...
S7 VMax Plus = Same as above but with auto empty dock
S7 VMax Ultra = Same as above but with the Ultra dock that empties the vacuum, washes the mop pad, and refills the mop water.

There's also the S8 series, but reviews coming in are saying that it's not quite as good at vacuuming as the S7 series.

The main advantage of the S8 series is that the high end models with object avoidance use a sensor array instead of a camera. If the camera is a big sticking point but you want the object avoidance and the dock with all the bells and whistles this would be the one to go with. As long as you don't mind an ever so slightly less effective vacuum. I personally do not think it worth the price premium over the S7 series. Definitely not worth it if you don't plan on getting the higher end models with object avoidance, but those models are required for the fancy washing/refilling dock.

I own the S7 Plus and I absolutely love it and so do my wife and kid. I have it well integrated with Home Assistant so nobody needs the MiHome app on their phone, they can just pop into Home Assistant and click the relevant button for the room they want vacuumed. I do however wish I had the VMax Ultra. You will have to stay on top keeping your floors cleared of things that might get caught in the brush. You will have to manually keep an eye on the water tank and mop pad to make sure you'll get a full floor cleaning. We have about 5 mop pads and just take the old one off and throw it in the washing machine each time the water tank needs to be refilled. It supposedly will alert you when the water tank is empty, but I think it has only triggered once and if it did work it would probably go off during cleanings most of the time. I have plans to get a water low alert going via Home Assistant based on square footage cleaned since the last tank removal, but i haven't gotten to it.

That said, my complaints are very minor ones that have more to do with not being able to afford replacing it with the pricier models. It has made our lives so much easier. We got a dog last June and I can't imagine keeping up with the hair without the vacuum. And the auto empty dock makes it much more convenient. The emptying mechanism is very powerful and can still empty the vacuum even if the bag in the dock has become a brick of dog hair.

Vacuum Wars on YouTube is one of the best sources of reviews for these things. https://www.youtube.com/channel/UCvavJlMjlTd4wLwi9yKCtew

Piggybacking your post a bit: Does anyone know a autonomous vacuum that does not rely on a cloud and directly integrates with home assistant only?

Personally I would stay clear of any of those Chinese robot vacuum companies. I am not giving them access to my home via a camera or other sensors.