Hello there,
We see you've posted about trying to sync apps that exist on your iPad to your iPhone. You also mention not using a Mac or PC to do so. The first thing to keep in mind that some apps on the iPad are not available for the iPhone (and vice versa). Also, certain developers have developed specific apps for iOS versus iPadOS.
There isn't a way to sync Apps between your device directly, but you can download purchased apps, even if they were free. Checking your past purchased apps on your iPhone would be the best way to then download them to your iPhone. If you don't see an app that exists on your iPad, it may be an iPadOS version app or for an iPad only. You would then want to search for the same app from your iPhone in the App Store app.
How to manually update apps on your Apple device
How to manually update apps on your iPhone or iPad
1. Open the App Store.
2. Tap your profile icon at the top of the screen.
3. Scroll to see pending updates and release notes. Tap Update next to an app to update only that app, or tap Update All.
All the best.