Do I still need to transfer everything to my new phone?

I went from and iphone 5 to an iphone 7. (I know, still kinda old) I had to do it for a reason not cuz I wanted to. I've only had it for 2 days. Either way, when I got it at the phone company they said that I had to do an icloud backup on my old phone so it'd be recently backed up so I could transfer all my stuff to the new phone. But the internet at my house isn't that great and the phone wasn't able to do the backup. I did try other places with Wi-Fi but it didn't work either.
What I did instead was just airdrop all the pics that I wanted from my old phone to my new one. And reinstall the apps I wanted. They're all the sign in kind, so I didn't lose anything. And my music got transferred over when I signed in with my Apple ID. Basically since I have everything that I wanted from my old phone, do I still need to do the backup?

If you've got all you need, then you're done!

Normally, a phone fully signed in to iCloud is constantly mirroring stuff like the address book, calendar and photos up to the cloud anyway, and are copied right back down when your new phone, tablet or computer are signed in, so even then you wouldn't need the backup if you're not doing much more than that. But it's good to have, you know?