Do you use iCloud Photos? Do you have Optimize Storage turned on? This will impact what backup does.
When you have so little free storage, it becomes really hard for the phone to operate, and even deleting files may become very slow or impossible. You should probably look at small things first, things that the OS has room to move around. See if you can delete apps, and especially app's data. Do you have stuff in Files?
Have you turned on Settings>Apple ID>iCloud Backup? If you have a recent iCloud backup, then you can certainly start over. If you have a computer, you should do a computer backup, as well. You can use "Settings > General > Transfer or Reset iPhone > Erase All Content and Settings" to reset the phone. To Restore:
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
“Restore” is what you do when you buy a new phone. Every time I've bought a phone, I've used restore and the phone was just fine.