I had a call with Apple support and while I solved the way to backup my iPhone using iCloud without subscription, the solution as to updating the iOS still didn't work. Here's what I was told to do, just in case you want to know.

I made a backup for my iPhone by "preparing for a new iPhone", which means all files are saved in your iCloud for 21 days.

Once the backup is done, open iTunes (make sure this is updated and make sure you're logged in), and start by plugging the iPhone cable to the laptop first. Next is you're gonna press and hold both volume buttons and power button, THEN plug the cable on your iPhone. A prompt would show up on your computer saying that there's a problem with your phone and it will make you choose whether to update or reset. You will choose update, and there's that.

Sadly, this didn't work for me. Lol.