Q: Question regarding app library in iTunes

You can use File > Add Folder to Library to import everything. or File > Devices > Transfer Purchases to import the apps on the device.

Moving libraries should be a matter of copying the entire iTunes folder, in which case all content should come over, and there should be no erase & sync warnings.

See also Recover your iTunes library from your iPod or iOS device. Make sure you backup the device before syncing and that the library has all of the content that you want on the device.

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1. You should have transferred the entire iTunes older as it was, not by content folder or type. This way the entire library remains together and cohesive, and can be easily loaded back into itunes. When transferring the library folder everything in it including Apps, books, media etc... is transferred over.

2. The Message you are receiving while it may have to do with the apps not being in the library because they were not moved, is fine, if you go ahead and transfer your purchases, whatever is not in the library will get placed there from the iPhone.  Its not a bad thing to do. And there really is nothing you need to resolve.

Re-download or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - Apple Support