I have an iPhone that is running out of space. I have added the Google Photos app and sync'd all photos to it. I deleted photos from the native phone app. That freed up space but now I have an issue with my Messages app. It has several gigs of space taken according to the storage panel in settings. Message is the number #1 app using my storage, a few gigs! I went into Message and deleted all of the messages but it did not register that the space is saved, so it still lists it in the storage panel as using a lot of space. I have about 20 megabytes left on my phone.
Go to Setting>Messages>Message History> Keep Messages> Choose 30 days. It will delete the ones taking up your storage. You can switch it back to Forever if you don't want your new messages deleted in 30 days.