iOS 13.1.2

Not sure about your car but to get rid of that Apple Pay nag, tap it to open it (as if you are setting it up) but then choose set-up later in the Wallet app.

Also, make sure Apple Cash & Double-Click Side Button is toggled off in Settings > Wallet & Apple Pay

After sending a complaint to Apple early AM (Oct 18, 2019 for the record) ~ I selected the « Finish setting up your IPhone » prompt (for 13.1.2 version),

then selected « Set up Apple Pay » and then...

selected « Cancel » at left top of my screen.

VOILA! No more red notification.

Will it come back, must be the next question. For now ~ & for the first time since the overbearing annoyance appeared, it is gone!

Fingers crossed, or I’m motivated to cut this small Apple screen addiction & try Android.

Re: question #2:

I just upgraded last week to 13.1.2. Tonight, after trying everything & sending a complaint to Apple.... I fell into the simplest of solutions to purge this annoying prompt:

Select both prompts, to update and to set up Apple Pay. (Ugh!);

Look at top left of screen for a Cancel option (seemingly to cancel the one action)...;

The red prompt is gone.

Will it return, or has Apple finally gone responsive on this nasty, insistent pushiness for more personal info?

To be seen.

For now, nada! Try it!