We have a basement bedroom/office that we have been unable to use because it shares a wall/door with an air bnb/studio apartment and you can hear everything through it. We are trying to make this a usable space on our side for a guest room or an office where you wouldn't be able to hear the people in the other studio apartment having a normal conversation. We own the whole house (both apartments) and have chosen to subdivide it in this way.

Just one of the walls is shared directly next to this attached studio apartment (the one on the right side of the picture). The other two sets of doors have the buffer of a closet then a bathroom on the other side. All walls consist of just studs and drywall, no insulation or anything. The shared door, which always remains locked, is a solid wood door but has some thinner panels and also an air gap under the bottom. This entire house was just renovated less than a year ago.

We are willing to spend some money on this space including possibly adding a second door as a buffer (but probably don't want to spend more than 1k on the door by itself). My initial thought was to extend the wall that has the closet doors across and add a second door between the two different apartments so someone can still get through in case of emergency. What kind of door should I use for this? The floor is somewhat sloped so I'm wondering how I can seal the gap that would occur under the door? I think the new wall extension would want to have insulation inside it, so if you have any suggestions for that, that would be helpful too. I'm also trying to figure out if I should add insulation inside the closet walls that are shared with the bathroom for the studio apartment, or maybe an extra layer of drywall with green glue, or maybe there are some cheaper foam panels we could use and just velcro them on the walls in the closet? Are there any other products that work where I wouldn't need to extend the wall and add a new door?

Thanks!