I've got my COE and all supporting documents. I have yet to get the covid test and fit-to-fly certificate. I've downloaded the "ThailandPlus" App to my phone and scanned through the intro. I'm not quite sure what I will be using this for, it's necessity, and how soon before my departure I should start fiddling with it.
TLDR : Answer Summary
The ThailandPlus App is necessary for registering health information and tracking during your stay in Thailand, although the fit-to-fly certificate is no longer required for travel. It's advisable to set up the app before your departure, but there is no strict timeline for when you must start using it.