[Story] Add a bot to a DM

### Description

* As a user who has a dm where I want to add a bot (or backup account)
* I want to use the mobile app EX to add this user but still keep the same DM
* So that I do not create a new room and keep it rendered as a DM

# Acceptance criteria
- Add a user to a DM and end up with a room with 3 participants. (not two rooms one with 2 participants and another one with 3)

# Dependencies
- None

# Out of scope
- Nothing

# Questions
- [x] None

# Subtasks

### Android
-

### iOS
-

### Rust
-

### Other
-

The issue names no files, tests, or entry points. Start by identifying the Android, iOS, and Rust client repositories and tracing the existing mobile DM flow in each one. Break the story into client-specific subtasks, then verify that adding a user leaves one room with three participants rather than creating a second room.

Written by the indexing model from the issue text.