Does transferring from my old iPhone to my new one, while they sit side by side, does that transfer everything from that phone to the new one or just what it’s set up to normally back up?

Apps will download from iCloud after the transfer of data and settings from one phone to the next. So in essence, yes, the transfer of data and settings is the stuff that is backed up.

Anything that you sync with iCloud may have to be turned on again of the new phone, but as I recall, all of my settings transferred correctly when I set up my new device. If you use Keychain for instance, passwords don’t transfer, but will be synced when Keychain is turned on.

Apps don't transfer from iPhone to iPhone, only the app data along with app links to the App Store gets transferred.

Apps & Settings --> Apart from the Apps following will also not get transferred.

1. Content from the iTunes and App Stores or PDFs downloaded directly to Apple Books
2. Content synced from iTunes, like imported MP3s or CDs, videos, books, and photos
3. Data already stored in iCloud, like iCloud Photos, iMessages, and text (SMS) and multimedia (MMS) messages
4. Face ID or Touch ID settings
5. Apple Pay information and settings
6. Apple Mail data
7. Apple Music