Backup iPhone without iTunes I recently dropped my iPhone in water and it was working fine right after that, but the next morning I was prompted with an ‘activation required’ screen. 

I’m afraid ‘activating’ will wipe out everything on my iPhone, so I’m trying to back everything up before doing that.

However, both iTunes and a third party tool called iMazing won't let me back anything up before activating.

I know that none of the data has been affected by the water because (a) it shows up in iMazing and (b) the lock screen still has my old wallpaper, language settings etc.

So, 2 questions: does activating my iPhone restore it back to factory? And how can I backup my iPhone without iTunes on Windows/Mac/Linux?
Question 1

The activation message doesn't mean it will do a factory restore, no, however it is possible that not all to the data will be retrievable even though you can see it.

Question 2

If you cannot get to the Settings app, which you can't from what you've described, then without activation there is no way to use iCloud to backup. iTunes would be the only option in this case.

Do you have an iCloud backup by chance?