how can I remove apps from the library

Not all apps can be removed. Some native Apple apps cannot be removed, for example. If an app is on your iPhone, it will also be in the App Library. You can't remove an app from the App Library and leave the app on your iPhone. Otherwise, y_p_w provided the right procedure to remove an app from your iPhone.

Note: If you can't remove any apps from your iPhone, go to Settings > Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases - Make sure Deleting Apps is marked Allowed

You can remove an app or offload it. However, if it's ever been downloaded, I don't know of any means to erase it such that it shows no signs that it's ever been downloaded.

Removal is usually by holding down the icon until the icons start shaking. Then there will be options.

Delete apps on your iPhone, iPad, and iPod touch - Apple Support

You cannot unless you remove the app from the iPhone . https://support.apple.com/en-us/HT211345