A Gen2 has major power supply problems .. same as Gen1.
You tested 6 other hard drives in the setup .. were any over 2TB? USB2 is usually limited to reading 2TB and less. You need USB3 to read drives larger than 2TB. Even with USB 3 not all USB works the same.
Seagate are really not the drives they used to be.. personally don't like them.
I still think that because the TC is giving you File structure on the disk.. but fails on transfer it means the disk is readable.
Spending a bit of money might still be worthwhile if the files are important to you.
There is two different ways to fix it.
Replace the power supply. Just type into ebay search Time Capsule power supply. You will find stacks of older Flextronics supplies.. you need the 34W version. They should be fairly cheap. $20 or so.
Or buy a Gen3 or Gen4 TC in working condition .. you might get them for less than $40 which makes it better buy IMHO than a new power supply. Open it up and swap the working disk for your 3TB seagate. Boot the TC again and see if it can read the drive and you can copy files off it.
Stop reading now if you don't want the lecture.
A TC is not a safe place to store files. If you have files stored on the TC and not backed up you should learn from this experience.. NEVER ever leave files on a single disk without backups. Disks die all the time.. backups die as well.. and precious stuff like photos can never be replaced if lost.. so multiple disks some offsite and cloud storage as well. Never be in a situation where you will have files not backed up.. loss of disk should amount to shrug of shoulders and purchase of a replacement and restore from backup.