Support Matrix URI scheme
Google allows apps to specify a custom URI handler, with the merge of the Matrix URI proposal, this means that the URI can be referenced from links, redirects, and other formats.
The URI handler is one missing part, but the more basic one would be support for interpreting Matrix URIs in the client itself. Currently if you e.g. write matrix:r/weruletheworld:example.org in a chat it is not recognized as a link.
Apparently when you currently open a Matrix URI scheme link opens FluffyChat iif installed and we just had a very good laugh offline for trying to open one 😂
Similarly, one could also consider sharing rooms/contacts as matrix: URIs, rather than centralized https://matrix.to links.