From what I can tell the last version where Live Edit on Mac (Big Sur) worked smoothly in Php Storm was 2020.3, worked great, very smooth indeed. Both 2021.1 and 2021.2 releases are really buggy where Live Edit is concerned. It works for a couple of lines of code, then stops??? I frequently get a message in the console when I type some code into the editor:
'Failed to load resource: the server responded with a status of 404 (Not Found) http://…63342/favicon.ico'
I know that's some kind of Chrome bug and I don't know if that has any bearing on causing the Live Edit to fail but I don't get that message when using version 2020.3, all works well - seems to be something introduced in versions 2021.1 and 2021.2 causing it, which is perhaps stopping Live Edit updating.