I've noticed that 2fa sign in process has an option to not use the 2fa the next time you sign in to the current website. It adds the website to the trusted devices list. It works good for me.
I set mine up to send the code to my device so it doesn't use the Samsung messages app. I really don't know which one is most secure but I prefer send to device.
I set up a sim card lock to require a pin code. I tried it for a while it's ok but adds another step when powering on.
I turned off cellular data and signed into this website with no issues.
The only real issue I've had in the past is that it was trying to use 2fa during the phone setup process after a factory data reset. There is no way to access the messages app at that point so I had to skip setting up the Samsung account and finish the setup. I recently factory reset and it seems the issue has been resolved.
OMG ME TOO!!! I am so sick of this stupid notification that I can't disable! I know I'm no help to you, but I just wanted to let you know there are others with the same situation. I have no desire to set up 2pa because of people I know that have had horrible experiences with it. I shouldn't be forced to use it if I don't want to, and I also shouldn't have to put up with the stupid notification. My next phone will be something other than a Samsung!