As designed Search button missing from 'Find Member' block

There is no need for that button.
As you start typing in the characters it automatically shows all combinations of possible names.
Click on the name.
 
Also bear in mind that JS disabled handling isn't designed to be perfect. It's designed to mostly/generally work. Smaller features may not work for example, particularly if there is an alternative (you can search for usernames via quick search).
 
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