Greyed out songs on I tunes

Gray songs can mean a few different things, so I’d first tap one of them and see whether you get a message such as “No Longer Available” or “This item is not currently available in your country or region.”

If you use Apple Music, also check Settings > Apps > Music and make sure Sync Library is turned on, and that Music is using the same Apple Account as your subscription.

Apple has a good breakdown of the different causes here: If songs are missing or grayed out in your music library in the Music app - Apple Support

I wouldn’t turn Sync Library off as a troubleshooting step yet, since doing that removes downloaded music from the iPhone.