DeclareUnicodeCharacter: Timed Out

You will find it easier to use such characters in xelatex or lualatex than pdflatex.

My (windows firefox) browser used a font called Ebrima to show the symbol in your question (as shown by selecting the "inspect element" menu option in the browser)

So I simply specified xelatex use the same font and the character "just worked"

documentclass{article}

usepackage{fontspec}
setmainfont{Ebrima}
begin{document}

abc ና xyz
end{document}

If you do not have that font, specifying whatever font you do have on your system that has that character would work in the same way.

For the actual error in the question, the package wasysym is not involved in any way here. The line

DeclareUnicodeCharacter{1293}{ና}

tells LaTeX that if it sees ና to use the code ና to typeset it, this is an infinite loop and on a system such as Overleaf that has a timelimit you would get a timeout error. If you run that on a local instance of pdflatex that does not have a timeout then it loops without filling up any stack so it will run forever until you kill the job.