Issues with iTunes and Apple Music

My desktop PC has iTunes installed, and my entire music library is loaded from an external hard drive that is always connected to the desktop. I can play all my songs on both iTunes and the Apple Music app on this desktop. However, on my laptop and iPhone, some songs in Apple Music are grayed out and won’t play. The error message says, “This item is not synced across your devices. On your Mac or PC, go to Apple Music or iTunes for Windows and in Settings, select Sync Library.” I have enabled "Sync Library" on the desktop, laptop, and iPhone, but these specific songs remain unavailable on the laptop and iPhone.

Additionally, I’m encountering another issue with device recognition. When I connect my iPhone 16 Pro to my laptop via USB-C to USB-C, the laptop recognizes the phone, but iTunes on the laptop does not. On my desktop, which lacks a USB-C port, I connect the iPhone using a USB-C to USB adapter, but the desktop does not recognize the phone at all, and iTunes cannot detect it either. Strangely, my newer Windows-based laptop (4 years newer) does recognize the iPhone, and iTunes on that laptop works with the device.

I need all my PCs and iTunes installations to recognize the iPhone. Additionally, I want my entire music library to be available and functional across all devices. Please advise on how to resolve these issues.