OK, I see. I have added this request to the tracker:
Issue 2343 – Site filter on Login dialog
You can vote for it there.

That's useful, but that's searching not filtering. It doesn't make the list/tree shorter. Which is important because filtering shows you when you typed in enough letters to identify what you are looking for. With searching you typically need to type in more and you are more likely to miss your target (if you remember the full name incorrectly and type in too much).

Just start typing while in the tree:
https://winscp.net/eng/docs/ui_login#incremental

In the current WinSCP 6.4 beta, the search function is more "discoverable" by popping up on Ctrl+F:
Issue 2281 – More obvious site search on Login dialog

Hi. So I have a lot of servers in various branches/directories. Would be nice to be able to quickly find a server by filtering by any apart of the name or folder name.

I imagine it working basically like Ctrl+S filter in the Total Commander.
An example of such tree filter in JS:
https://fiddle.sencha.com/#view/editor&fiddle/2qq9