On the latter case Mozilla runs one. There are tables of free ones on the Internet, and you can also host your own.
On the former it isn't clear that the matrix.org software was to blame at all.
All features of synapse are currently not there. For example, most media APIs are not working, like URL preview. Before 2 months ago, I feel like they were making great strides with the project. They were pushing out weekly updates.
Development has definitely slowed down, and it doesn’t help one of the key contributors/maintainers has left the company/project.
Hopefully the project gets a few dedicated maintainers and people to manage and fund it. It really is a great implementation but I ended up switching back to synapse.
I recommend setting up a separate instance and subdomain.