Availity to completly move DM from home to personal Space

**Is your feature request related to a problem? Please describe.**
I moved some room and DM in my personal space but from home only room is moved not DM. And now the room and DM in Space also those DM is present in my Home.

**Describe the solution you'd like**
I wish to move my DM as like room. I don't want to see this DM in my home I only want to see it in space. This way I can organize my DM too as like room.

**Describe alternatives you've considered**
There can be option like room "Show all rooms in home". For DM it can be "Show all DMs in home".

**Additional context**
Add any other context or screenshots about the feature request here.

No files, tests, or entry points are named. Start by tracing how moving rooms between Home and personal Spaces controls visibility, then compare the current DM behavior; done means DMs can be organized in a Space without appearing in Home, with an option comparable to “Show all DMs in home.”

Written by the indexing model from the issue text.