Now, I believe that all I should do is turn off the "Auto Park Brake" option, so that the park brake is not applied when vehicle is turned off, and I can do the replacement.
I'm not so sure about that. The procedure (which looks like it applies to both manual and automatic transmission ("transmission must be in park or neutral") is more than making sure the EPB isn't on -- because that's just the first step. The rest of the procedure would completely retract the piston.
I would go through the steps, and see whether your EPB fault light flashes -- that will confirm that the procedure is successful.
By the way, as complex the Renegade is, if I were you I'd really want to have a Owner's Manual, at least in soft copy. For U.S. versions, they're available for download here -- this is for a 2021:
2021-jeep-renegade.pdf
If you're not sure what year yours is, you can look on the data plate that's inside your driver's door frame on the B pillar -- at least, yours should be in the same place as mine:
That gives the month and year of manufacture (not necessarily the model year) -- mine is 02/21 (circled), or February 2021.
Yes, I can from your profile... flag of Macedonia -- er, Former Yugoslav Republic of Macedonia -- er, Northern Macedonia...
You guys must be so confused.

But:
Where are you in Macedonia? I was deployed there as a civilian for three months at the very end of 2001, working from the Defense Attaché Office at the U.S. Embassy in Skopje. That was right after 9-11, and right at the end of the civil war you guys were experiencing with the Ethnic Albanians in the mountains around Tetovo. A couple months before our Embassy had been attacked and partly-burned (some vehicles, anyway) by an angry mob. We were very worried about such things in Europe. And no one from the permanent Embassy staff were regularly traveling up into the mountains to see what was really going on (not even the guys who should have been); so my partner and I were making regular trips all around there.
Beautiful country -- very beautiful. And nice people everywhere (unless they were pointing AK-47s at me

, which happened a couple of times).
I actually met Vlatko Stefanovski there, who was a childhood friend of my landlord. He's still one of my favorite musicians, and I think one of the world's great guitarists...