External Portable SSD - Disk Utility: "The partition map needs to be repaired because there's a problem with the EFI system partition's file system (-69766)"

Make sure your data is backed up before doing anything else.

You can try restoring the partition table using the backup partition table by using the command line using the "gpt recover" feature.

If the external drive is using the HFS+ (aka MacOS Extended (Journaled) )file system, then you can try using the paid app Disk Warrior.

Otherwise you will need to erase the whole physical drive as GUID partition and MacOS Extended (Journaled).

Personally I wouldn't trust a drive with damage to the partition table or the file system. It is up to you whether you feel safe using the drive this way. Just make sure that you have a good verified working backup of any data on that drive in case the drive becomes inaccessible at some point.

For reference I recently had one of our organization's laptops which would crash my Mac whenever trying to connect the laptop to my computer to retrieve data from it using Target Disk Mode. Once I was able to find a way to boot the faulty laptop I was able to run Disk Utility First Aid on it and Disk Utility said everything was "OK". But examining the details I saw Disk Utility report lots of unfix errors. Disk Utility is not the smartest app and in fact is quite pathetic at its job. This was the only problem with the laptop --- a damaged file system and it was almost impossible to access the data since it also prevented the laptop from booting into Internet Recovery Mode. I was very lucky that I got it to boot from my external macOS USB drive to recover the data.

Only you can decide how important the data on the drive is and whether you have a reasonable number of backups in case several things end up failing at one time.

Disk Warrior is the only app which will may work (no guarantees) and is well worth the cost if you need access to the data on the drive. I would not trust any other app. Our organization used DW for almost 20 years and while we did use some other apps once in a while DW was the best and most reliable.

Keep in mind that Disk Warrior does not work if the drive to be repaired is using the APFS file system. In fact there are no utilities capable of repairing the APFS file system since Apple has not yet released the necessary documentation.

Sometimes DW will detect a hardware failure and will refuse to repair the drive which is a good thing since attempting to repair a file system on a defective drive could cause more problems for a professional data recovery service to access the data.

Any time you use a utility to manipulate the partition table or file system you risk making a problem worse. DW does have a preview feature which is supposed to help in deciding if the changes are Ok before you allow DW to make the actual changes, but I don't know if the preview would apply to changes in a partition (it has been a long time since I last used Disk Warrior). DW won't damage the physical drive, but DW could potentially make the drive so it cannot be mounted within macOS. I've never encountered this even when the file system needed lots of repairs which required several passes with DW, but there is always a risk no matter how slim.

I'm just a regular user such as yourself who happens to support thousands of Macs in our organization. Besides I don't think the moderators would allow promoting a business on these forums.