Gemeindebürgerrechte processing time

How long does the Gemeinde need to process the naturalisation application after receiving it from the Kanton?

They informed me that in my case it is rather just an administrative process due to my studies here and my German knowledge.

My application had been received yesterday, I have informed them that I will be moving out of St. Zh by October and they are confirmed that they will be dealing with my application with priority due to the moving situation.

Can i then freely move after they have processed my application?

Various people have posted their timeline here: https://www.englishforum.ch/permits-…-diary-71.html