I am experiencing the same problems and it is a pitty that Adobe wasn't prepared in any way. My Illustrator is shutting itself down and I get multiple error messages. The working process is very influent and difficult since the programm freezes all the time. Please fix this with a quick release of a beta version.
We're extremely sorry to hear about the trouble you are facing with Illustrator on M1 device. I have branched your query from an old thread so that we can look into this issue more clearly. To help you further on this, I would need a few more details like:
Version of Illustrator. On the last post, I mentioned to install the latest version 25.1 to fix performance related issues on Illustrator. Please confirm if you have already installed version 25.1. If not, please install that from CC and let us know how it goes.
If you are already on 25.1, please share more details about the issues you are facing. For example, if the issue is related to a specific document? If yes, could you please share the document with us? You can upload it to the Creative Cloud (https://helpx.adobe.com/in/creative-cloud/help/share.html) and share the download link.
Where are the files saved (Network Drive/ System HDD/ Shared Folder on System /External HDD)?