Refactor and clean up our ambiguity handling

[poljar]

This is in preparation of some higher level user display name handling, thus the rename of our DisplayName type as well.

No functional changes here.

[codecov]

Codecov Report

Attention: Patch coverage is 98.00000% with 1 line in your changes missing coverage. Please review.

Project coverage is 84.85%. Comparing base (237419c) to head (b89c409).
Report is 6 commits behind head on main.

Files with missing lines	Patch %	Lines
crates/matrix-sdk-base/src/rooms/mod.rs	66.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4218      +/-   ##
==========================================
+ Coverage   84.83%   84.85%   +0.01%     
==========================================
  Files         273      273              
  Lines       29525    29530       +5     
==========================================
+ Hits        25048    25057       +9     
+ Misses       4477     4473       -4     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[bnjbvr]

Thanks!