Matrix

I am interested in trying out matrix, but my first impression seems to reveal that by default, there may be some privacy or anonymity pitfalls if I use matrix.

Examples:

• using an instance I don't host means the host is trusted with my data
• self hosting might reveal a lot of information about me. Most likely, it is registered to a domain that has my info and could potentially be traced back to me.
• When self-hosting, being one of few users, basic analysis of my activity could reveal a lot about me, since all that activity could be easily identified as belonging to a single person

Now I understand not all threats could be mitigated, but my worry is that both self hosting or not have significant gaps. What's the most privacy and anonymity conscious way to use Matrix?