I have my photos library on a external 2TB SSD and I get an error claiming there is not enough space on my local drive, why am I seen this?

In addition to the format of the file system pointed out by Yer_Man, you will have to keep the external drive with the Photos Library connected and plugged into your Mac at all times, while you are signed into your user account, or Photos may lose the connection to your system Photos Library and create a new System Photos Library on your internal drive.

You can check, which Photos Library is currently in use by Photos by looking at the Photos > Preferences > General. The top of the General tab has a button to show the current library in the Finder. Where is it?

And a second problem is, that we always need twice the size of the library as storage on the disk with the library and also in iCloud, if we have to enable iCloud Photos again after a system upgrade, after a library repair (because of crashes) or when Photos lost the connection to the System Photos Library. When Photos has to start over with syncing a library with iCloud, it is estimating the required storage based on the worst case assumption, that all items in the local library are different from the items currently in iCloud and will not start syncing again, unless you have enough free storage equal to the size of the library in addition to the storage used by the library. So do not toggle iCloud Photos off and do not try a library repair, unless you have enough free storage.

Which system version is installed on your Mac? Since the upgrade to macOS 15 Sequoia my MacBook Air is using more storage for the local copy of the library than before. The amount of storage for working copies in the library is a bit larger than before. My library has grown after the upgrade from 312GB to more than 400GB.

What format is the external? It needs to be formatted Mac OS X Extended, Journaled or apfs.

but since when did it have to be foraged OSX Journaled?

Note that I said Mac OS X Extended, Journaled or apfs. Apfs is just fine.

but yeah its weird for apple or anyone to suggest the format of the drive must be other then AFPS since they ship photos library on a AFPS with every m1 Mac,

Mac OS X Extended, Journaled predates apfs. And many older Macs require it still. So, not so weird :)

I will defer to whatever it is that you're saying in the next two paragraphs, as it doesn't make a lot of sense to me, and Macs are significantly less expensive than when Mr. Jobs ran the company.