Beta update is not showing up in my iPhone 7 Plus

There is nothing to do. iOS updates, public or beta ended long ago for iPhone 7. iPhone 7 is capable of being updated to iOS 15.8.3 and no higher. It is too old and lacks the hardware to be updated further.

There hasn't been a beta available that will run on an iPhone 7 Plus in years.

You won’t be able to test any Beta updates on your iPhone 7 Plus. Any beta updates currently would be iOS 18.4 or later. Your iPhone 7 Plus can only go to iOS 15.8.3 and no further, your Beta updates ended a while ago.

You can update an iPhone 7 Plus to the latest release of iOS 15 – currently iOS 15.8.3.

You cannot – and never will be able to – update an iPhone 7 Plus to iOS 16 or higher. If you are running iOS 15.8.3 now, the reason your iPhone is not showing you any updates is that there are no more updates, as of today, for your phone.