photo Library recovery form exfat jetdrive card

You've been lucky, and now your luck has run out.

A Photos library has to sit next to a volume formatted Mac OS X Extended, Journaled or apfs. If it's put on an inappropriately formatted volume issues arise eventually - as is the case. Among those issues is silent corruption of the library, leading to the kinds of issues you are seeing. This is not a Tahoe issue, this has been the way since the app was released.

First step: move the library to an appropriately formatted volume. If you're lucky that will solve your issues. If not post back and perhaps we can help you more.

I would also point out that Apple advise against placing the library on small cards such as this as it believes them to lack the robustness for the housing the library.

esanudo wrote: … I cannot … even copy it and paste it into the macbook harddrive.

That is certainly disturbing! Usually a Photos Library package on an ExFAT drive can be copied even though it can't be used while on there. It may be that you need to use the Mac's Disk Utility to examine the card and use First Aid on it.

Do you have backups for this Library?

esanudo wrote: …wow, I have been using the photo library like this since I got my previous computer in 2015! I never had an issue.

After my father's first heart attack he said, "Well, it worked fine until now!" Sometimes there is corruption that you can't see until it catches up with you.

What to do now: The Photos Library is a "package," a folder of related stuff that doesn't open like a regular folder. The reason this package thing is used is that even seemingly small disruptions in the organization, permissions, etc of the contents can make the Library completely unusable-- so the package discourages prying fingers. If we ever decide to go inside of the Library package, we have to be sure we have a backup copy, because we might accidentally contaminate the contents. It seems that's not a worry in your case.

If you right-click on the Library package, you get a menu that includes "Show Package Contents." In there is a folder named "Originals" that has all the picture files that were loaded into Photos completely untouched. Well, the names have been changed-- otherwise there might be 7 files with the same name, like IMG_0123 or something. But dates and other metadata are fine, so you can load these "Originals" files into another Photos Library and they will look fine. Edits you may have done on these pictures are stored as instructions in the database, so they are lost. If you look around, you may find lower resolution "preview" versions that show the edits for some pictures, however.

As you go forward you need to know: If you use iCloud Photos, then the System Library, the one that synchronizes with iCloud, needs to be kept on the internal drive. This is because you're using a laptop, and synchronization can get confused by plugging in and unplugging the Library's drive. (For a Desktop Mac, with no need to unplug the drive, an external drive is just fine.) The tiny "jetdrive" was a clever solution since it could stay plugged in all the time-- but the downside was not just due to its incompatible format, but also because those things are excruciatingly slow, and they are not very reliable-- as you've seen. But it's OK to use non-System (iCloud)Libraries from an external drive.

If your Photos Library doesn't fit on your MacBook's internal drive, you have some options.

• One of the first things I did as my storage started to fill was to transfer any files I didn't need much to an external drive so I could keep my Library on the internal drive. Eventually most files not connected with photography or daily use ended up on an external drive. I put work stuff on an external drive. I use a small (1 ounce!) external solid state drive (SSD) that's fast, reliable, and small enough to carry around with no trouble. (I also carry another one like it with Time Machine backups on it.)
• Another option is to use iCloud's "Optimized Storage." This relies on iCloud to hold the large original picture files while the Mac keeps thumbnails and preview versions that take up as little as 10% of the space for the full Library. When editing pictures, Photos grabs the original version from iCloud. The downside here is that, with Optimized Storage, the full originals aren't available on the Mac for backups. A backup of the Mac would just copy the low resolution versions that are on the machine. Here's a solution to that:

Backup iCloud Photos with an Optimized Mac - Apple Community

• You can have several Libraries on a Mac. So you can keep a smaller Library-- maybe just favorites or just recent pictures in a System Library on the Mac, and keep all the others in a Library on an external drive.
• And, of course, if you don't use iCloud Photos at all, then you can keep your Library on an external drive that you carry around with you.

What do you think?

the card was 256 Gb, not so small in my opinion.

The capacity of the card is not what matters it's the physical item. That's what's small.