I found a comment from dansup in issue 5885 on the Pixelfed GitHub. The inability to tag users on other instances is by design.

I edited my post to include this info.

Nope, it doesn’t work. I can manually type your username into the search box, but nothing appears. To be clear, I’m talking about tagging someone in a picture, not a comment. If it makes a difference, I’m using the Pixelfed website, not an app.