Problem syncing my playlists from iTunes for Windows to my iPhone

I have an iphone 13 and use my own library of music (no subscription to Apple Music). I share my library between this iphone and two PC's. The other day I realized that some songs I purchased and placed into a playlist on one PC (the Dell) did not show up on the iPhone via wifi sync. I tried to sync the iPhone using a USB cable but it starts out with a backup and there is not enough space on the Dell hard drive to backup the entire iPhone. So, I backed it up to the other PC (the HP). But since the HP has its own separate library and we just home share the library on the Dell, the sync did not populate the playlists. I have tried reinstalling Music and re-syncing and the best I can do is get all the original songs onto the phone. My playlists simply will not get populated. How can I resolve this issue and recover my playlists?