How to reset an unused iPhone 13 without remembering passcode or Apple ID?

OK- If you've forgotten your iPhone passcode – Apple Support (UK) is the only way forward if you do not know diddly-squat about the MIL's handset and your MIL is incommunicado.

It was pretty straightforward, once I figured out that the download will continue even if you cannot see/find it anywhere* after the phone exists recovery mode after 15 minutes.

*No sign of it in Downloads, no sign of it doing a search for it by name and NOTHING at all showing in the Activity Monitor's network tab either.

In the end I calculated how long would still be left to run if I subtracted the 15 minutes from it and lo and behold- it worked. The restart of the phone in recovery mode while plugging it in auto-initiated the install just as it had auto-initiated the information that either an update or restore would be required for the phone.

Interestingly I noted that the setting of the passcode (and Face ID) comes before the setting up/signing into an Apple ID. Which is what I found hard to believe, as that is counter-intuitive. But, at least, that meant that my BIL was right when he said that they'd not gotten that far with it all.

All good now.

Thank you so much for that info. It made me take a look at my options, and I actually found the Apple Way: If you've forgotten your iPhone passcode – Apple Support (UK)

Only problem I am now facing is that the phone exits recovery mode after 15 minutes and the download from Apple which is required takes much longer with my snail-speed internet. The instructions tell me to let the download complete when that happens and to restart the phone, but I have no idea if it is still downloading as the interface changes and there's no process bar. Blast...

Sorry- I'd not seen your reply. Thank you for that- I had found the link for the reset (If you've forgotten your iPhone passcode – Apple Support (UK)) doing a Google Search and it would work if I could be sure that the download's still happening even after the 15 minute exit pattern for the phone. Assuming that it does, I will try it again tomorrow and see if there's no requirement to download anything still. Fingers crossed!

Oh, absolutely- thank you! Besides giving me the idea to do a Google Search for solutions outwith Apple (and the result promptly returning me to Apple for the solution), I did have to smile because you read like me- tirelessly trying and having to sleep at some time, only to find that it had worked when you woke!

I think that you ended up doing pretty much what Apple tell you to do, because this is what I was told:

1. Power off your iPhone, prepare use of a computer (Apple device or Windows with iTunes),
2. Plug in the charging cable to your phone and prepare to power on by holding the correct two buttons (with a 13 that is the power button the right and the - volume button on the left) while plugging the other end of the cable into the computer, holding the keys until you see the recovery mode icons (plugged in cable from bottom of screen etc).
3. Then locating the iPhone in either Finder or iTunes (for me, running Monterey on a Mac, that was in Finder) on the computer, selecting it, and-
4. opting to restore it, not just update it.
5. Then heed the screen. The download should be in the 5GB to 8GB range and there should be a status bar somewhere to tell you how you're doing and how long it will take. Bearing in mind that recovery mode only lasts for 15 minutes, be ready to let the download run as is (without the phone being in recovery mode after 15 minutes) for the remainder of the download time, before-
6. unplugging the cable with phone from the computer, shutting it down and going through step 2. above again. The result should be that instead of being told that you need to download something, you should be told that the update's being installed. Yay!
7. Follow the remaining instructions.

It's really easy as pie once you know how and it's Apple's own instructions you're following (no trust issues for me, you see)!

Oh- there is some progress in that I have an unusual error message when trying to reset the suspected email address as Apple ID's password (since that should trigger an email to the registered email as part of the password reset, should it not?):

Could that be indication that it may BE the right email but that they have well and truly wrapped themselves into a knot?

It gets worse- my brother-in-law, who set it up, doesn't know whether he set it up as his phone under his Apple ID. And, worse, he cannot confirm his Apple ID. Because I cannot even find it when I try the email which he tells his brother (oh brother... See what I did there?!) is his. So- not only do they all not know the passcode set for the phone, they do not know the Apple ID it uses, nor do I have confirmation of any viable Apple ID at all.