iPhone not backing up, overfilled with photos, will not work and can't lose photos

iPhone 8 ios 12.4 64 gb

To MacBook air (2017) running monterey 12.2.1, newly upgraded from Mojave 10.4(?)

Running into issues backing up an iPhone.

My goal is to back up an iPhone to a Mac with the intention of factory resetting the iPhone after.

the phone is full on storage, too many photos to the point that the phone will insta delete received text messages, drop calls, and no longer allows for photos to delete. When an attempt was made at clearing space by deleting larger videos, after the delete process, a white image with a play button that did nothing filled the place of the video. Issue also happens with smaller photos now, tho i don't think it did before.

I'm running into many road blocks, if anyone could help with any of them it would be greatly appreciated.

There is not enough storage on the laptop to back up the phone, it tells me when i plug it in. When i actually click on back up, it asks if i want to encrypt the data.

If i hit yes, it prompts me to enter and re enter a password to set it up, and whenever I attempt to it returns "the password could not be set up.

If i hit no it will attempt to and quickly return that it could not be completed as the iPhone disconnected.

The cable is good, the USB works.

I have tried turning on restrict background app refresh, airplane mode, and low power mode simultaneously, same issue. It says there is 78 gbs available on the Mac when i go to the storage tab, but only 40 gbs when i go to disk utility and look thru them all.

⚫⚪ How can I get it to back up/ do i need an external hard drive? ⚪⚫

Second issue

I had an external hard drive, Mac compatible, so I partitioned and set up time machine with 1 TB of storage and made two other partitions, one for photo back up and one for iPhone back up with 500gb each. I'd like to keep the whole phone backed up to put back on her phone after a factory reset, and I'd like to back up all of the photos on it(and teach her how to) to prevent the issue from coming back in time as she has a habit of doing this to phones.

The storage on the Mac is taken up by stuff that can't really be moved to make any meaningful amount of room, and i don't see an obvious way to find the files folders and move them anyways.

⚫⚪Is there a way I can have the iPhone back up sent to the hard drive? ⚪⚫

I saw an online article saying i could do some folder renaming and typing stuff in terminal with "sudo" before it, with the intent of tricking itunes to back up to a different location. I'm hesitant to try that for fear of messing it up and not even knowing for sure that itunes or whatever system backsup the i device will see that there is storage in the folder location, or if it will just check the system storage and deny it again.

I'm also running into an issue where it will import all but one of her photos and like 6 what appear to be corrupted video files? They are white and non reactive with a play button on them. Why won't it back up that last photo? I copied the photos app the hard drive and opened it thru finder, then redirected it to a folder i made before updating from Mojave to get the photos to import to the hard drive.

I tried to copy itunes on Mojave but that didn't work, and the application is still unreachable in Monterey.

Another issue I'm running into is that the amount of photos I've gotten to upload does not equal the number displayed on the phone, it's a thousand short. When i add the amount in her icloud (5gb) (i am so sick of the word icloud) it is over the number it says on the phone. I can't easily download all of her icloud photos easily to see if it recognizes the over lapping files, even with CMD+a, because it only lets me move 1000 at a time and there are 1500 photos, how can I select, say half of them to take an action on.

I am dog tired of trying to work with this system, i have light experience with windows and almost none with apple products. Honestly any kinda of direction would go a long way. Her phone is almost unusable at this point, and there isn't a lot of money in the budget to get a new one, and the photos are extremely valuable as they are all of her newborn child.

I'd like to do this without paying for i cloud if possible.

Thanks in advance

-Y