Can't download an app even after deleting everything

I'm switching from an iPhone 6 Plus (16GB of storage) to an iPhone X. The only thing I'm interested in transferring is my WhatsApp data. Issue is, a couple of days ago my old phone decided to uninstall WhatsApp due to lack of storage, therefore I can't upload my WhatsApp data onto my iCloud and transfer it to my new phone. I figured the only solution was to delete everything on my old phone except for WhatsApp with the hopes that I'd have enough available storage to reinstall it. After hours of trying a million options to safely back up my photos and delete them from my old phone (and from the "recently deleted" file), WhatsApp still won't install. I've deleted every single app except for the ones that can't be deleted. Is there a solution to this, or will I just be forced to start WhatsApp from scratch on my new phone and lose years of meaningful photos and messages? Thanks in advance.