You should quarantine them until you’ve analyzed them.
Like you stated, an async process using a function would suffice. Previously used ClamAV for this in a private cloud solution, I’ve also used the built in anti-virus support on Azure Blob Storage if you don’t mind multi-cloud, plus an Azure Function has the ability to support blob triggers, which is a nice feature.
The file types scan is relatively simple. You just need a list of known “magic string” header values to do a comparison, and for that you only need a max of 40 bytes of the beginning of the file to do the check (from memory). Depending on your stack, there are usually some libraries already available to perform the matching.
And it goes without saying, but never trust the client, and always generate your own filenames.