I bought more space but it’s still not letting me update

iCloud storage does not add space onto your device, it is Apple's cloud storage system you can use to store things such as backups and photos.

If you're getting any error messages when trying to update your phone please let me know so I can help you.

If you go into iPhone Storage is anything unusual? You might want to delete apps which take up a lot of storage which you don't use or enable Optimise Photos which allows you to save high resolution originals of photos on the iCloud storage you have bought so it's always there, while keeping them in lower quality on your phone

Sounds like your device is out of storage, in which case, see the following --

https://www.youtube.com/watch?v=bnhuHSv_WrI