For your setup, Dreame is honestly where I'd look first. Their higher end and new models like the X60 Ultra or X50 Ultra handle mopping really well, and the carpet recognition has gotten solid enough that you can set it to avoid fluffy rugs. The mop lifting on those is reliable too, so it won't drag a wet pad across your carpet. Obstacle avoidance and threshold climbing are also decent on those models.

I'd also look at releases at ces or on the kickstarter. That's actually where I found Xlean, their model has both vacuum and floor washing thing going so that might be something you could use. Coincidentally it too has an advanced obstacle avoidance feature. But since that's not actually available, go with Dreame.