Ihave a large PHOTO library (75 GB on a desktop mac. Is there a way to transfer it to my iphone 15?

What happens with iCloud Photos when you connect your Mac to iCloud is that all the pictures in your Mac's Photos Library, with album organization, edits, and metadata, are copied to the iCloud Photos Library. If your iPhone's Library is connected to iCloud (iPhone>Settings>Photos), then all the pictures from the iCloud Photos Library are copied to the Photos Library on the phone. You can choose, if you like, to copy only screen-sized images to the phone (in Settings>Photos>iCloud>Optimize Storage) to save storage space on the phone. Or, if you have plenty of space, you can choose the copy the originals in full size. Then you have three Photos Libraries that all stay in sync as you add, edit, or delete pictures.

You don't actually have to keep the Mac Library-- many people with iPhones don't have Macs at all. So if you disconnect your Mac from iCloud (Mac>Photos>Settings>iCloud), then you can trash the Photos Library with no repercussions. If you open Photos again sometime, it will create a new empty Library. If this is not connected to iCloud, then it will remain un-connected from your iCloud Photos Library and from your iPhone Photos Library.

If you connect an empty Library to iCloud, then it will re-fill with the pictures from iCloud. Again, you could choose to Optimize Storage on you Mac to keep only smaller sized images on you hard drive while the original pictures are kept in the iCloud Photos Library.

Many of us actually keep two Libraries on our Macs-- one that is connected to iCloud, and one (or maybe more) that isn't.

Yer_Man suggested that you keep your Photos Library on your Mac, in part because that's the only way you can actually back up your Photos Library-- if you have "Download Originals" checked in your Mac Photos iCloud settings. Most of us have a local Mac Photos Library that has the originals, and we back that Library up with Time Machine or some other system. Keep in mind that iCloud is a synchronization service, not a backup service. It synchronizes mistakes as well as pictures, so it's best to have a "pre-mistake" backup on an external drive.

Depends exactly on what you're asking here. You cannot transfer a Photo Library from a Mac to an iPhone. What you can do is sync the library to the Phone is you have enough space on iCloud. This will still leave the library on the Mac, where it should remain. Can you clarify exactly what you're asking?