I noticed a bug in the Steam client.
I contacted support about this issue (Reference: HT-K36D-PQH7-MHNQ), and they suggested I create a post here.
I have a friend named "Тест," for example. I'm changing their name to "Леша" to make searching through my friends list easier. The only problem is that searching through "Friends and Chat" (the button in the lower right corner of the Steam client) works correctly if I enter "Леша," but if I enter "Леша" through the "Friends" page, the search doesn't work.
This doesn't work with all usernames. I suspect you've technically entered an incorrect Regex for your search.