iCloud & iCloud Photos · iCloud Photos and the Photos library
What should an external drive be formatted as for a Photos library?
Short answer: Use APFS (or Mac OS Extended on older setups), on a drive connected directly to your Mac. Avoid exFAT, network drives, cloud-synced folders and your Time Machine drive. Check the format in Disk Utility.
Use APFS (Mac OS Extended also works on older setups). Photos expects a Mac-formatted drive that's connected directly to your Mac. Avoid exFAT or FAT drives, network drives, and folders synced by a cloud service, which can cause errors or damage the library.
Also avoid the drive you use for Time Machine — keep backups and your working library on separate drives.
You can check a drive's format in Disk Utility. Reformatting erases a drive, so copy anything you need off it first. See external drives.