My iPhone13 has been unable to install iOS 26.3 / 26.3.1. It is always left on charge, and I am confident it is always connected to my WiFi. There is 80Gb storage available. It never is able to tell me why the install failed. Frankly, if you have a feature, then it should work (what's the point otherwise?).
(FYI, I had a phone - i15? - for work, and it installed iOS 26.3 in ONE attempt)
iPhone 13, iOS 26
Did you try to set the iPhone back to factory settings? This should install the latest available iOS software automatically:
Restore your iPhone, iPad or iPod touch to factory settings - Appel Support
Can you see the iOS update starting and the progress, when you tap on "Update Now" instead of "Update Tonight"?
Update the iOS software on your iPhone, iPad, or iPod touch - Apple Support
I might as well do a manual update. The phone says it will do it automatically, but it doesn't. It doesn't tell me why it didn't do it.
iPhone 13 unable to install iOS 26.3/26.3.1 updates
