The latest Kindle update broke the jailbreak even if it was installed, so you'll need to stop updates. You could just leave it in airplane mode, but not being able to use the internet to pull down books from your Calibre-web server means you may as well just send books via Calibre.
I'm planning on getting a Kobo Clara BW when my Kindle dies (it's currently got holes at the corners and a few dodgy-sounding rattles so soon™). Then I can use Koreader+Calibre-web to download books and sync read state like you can do with Amazon.
So your process here is get comics -> comictagger -> upload to server and kavita, correct?
Pretty much, apart from that I often add them and only fix if necessary, e.g. they're not going into series properly.

I guess I've just been lucky then! I've stripped DRM off everything else, so I expect theirs would come off using the same tools.