Data Transfer

Tomorrow, I’m switching my iPhone 8 to an iPhone 13 mini, and I’m also switching from T-Mobile to Verizon. I’m guessing they’ll take out my card and put it in the new phone, like they did before when I switched from an iPhone 6 to an iPhone 8. Last time, all of my TikTok drafts from the iPhone 6 transferred over to the iPhone 8, and basically everything I had on the iPhone 6 was transferred to the iPhone 8. I didn’t have to redownload anything, or have to save anything from the old phone. The home screen and lock screen still looked the same as it was on the iPhone 6. The iPhone 6 said it was backed up, so every single thing from that phone transferred over to the iPhone 8. Is this the same when switching from the iPhone 8 to the iPhone 13? Does switching phone providers complicate anything either? I would like to know so I can save my TikTok drafts or screenshot my home screen and lock screen beforehand. It also doesn’t help that on this iPhone 8, I have 64 GB of storage, and it’s almost full (at 63.5 GB). I’m switching to 128 GB, so storage won’t be a problem then, but it would be hard to save TikTok drafts right now if they don’t switch over because I would have to screen record them. I would just like to know if everything will stay the same, because I am very paranoid and scared about losing certain things. Thank you!