Tahoe 26.0.1 Seagate External Hard Drive Install Driver Loop

This is why generally it is advised to not utilize third party disk utility software.

Hopefully you can find an older Mac with an older MacOS that this Seagate software still works with, mount your drive, copy off all files, then erase/format the drive, completely uninstall those third party drivers and disk software, and then restore your files.

If you can't find such a Mac, try contacting an Apple Authorized Service Provider. They can probably do this for you, probably for a small fee. They are certified by Apple but since they are independent shops they have more flexibility to deal with such odd situations versus Apple Stores.

You have one option left with two ways to perform it. You need to run the Seagate software and turn off the SSD's built-in hardware encryption feature.

Two methods to achieve that goal:

1) If your Mac has at least 100GB+ of Free storage space, then you can create a new APFS volume & install an older version of macOS onto that new volume so you can run the proprietary Seagate software to turn off the SSD's built-in hardware encryption feature. Ignore the "Available" storage value shown everywhere in macOS since it is not synonymous with Free. The Free space value is only shown within Disk Utility. Assuming your Mac can run Sequoia, then you may need to create a bootable macOS Sequoia USB installer.

If you don't have 100GB+ of Free storage space, then you can install macOS Sequoia onto an external USB3 drive instead. Boot from the external drive & install the Seagate software in order to turn off the SSD's built-in hardware encryption. See the following Apple article for details since installing macOS onto an external drive on an M-series Mac is a bit tricky regarding the DFU Port issue:

How to use an external storage device as a Mac startup disk - Apple Support

2) If you have access to a Windows system, then you can install the Seagate proprietary software on that Windows system so you can then turn off the SSD's built-in hardware encryption. If it is not your Windows PC, then you may have a time convincing the owner to allow installation of an invasive app onto their system.

After this process, your Seagate drive will no longer be encrypted. If you want the data on that drive to be encrypted, then you may erase the drive & use an encrypted APFS volume followed by restoring the data, or use a third party option such as VeraCrypt.....the latter could still be an issue since it relies on third party software again

No matter what you choose to do, you should make sure you have frequent & regular backups of all external media just in case you are unable to decrypt the encrypted volume/drive. If you cannot unlock an encrypted drive, then there is no way to access that data unless you have the encryption/recovery key (assuming the drive is healthy).

IIRC, in the thread where @Psych13 posted what turned out to be only a temporary solution (if not there, a similar thread), advice was offered to the effect that, once access to the drive was regained, the next step was to copy the data off the external drive, completely erase the drive with Disk Utility to remove all vestiges of the 3rd party software controlling access, then format the drive and apply encryption with Disk Utility if desired.

Unfortunately, I have no suggestions for how to regain access to your data, but if you are able to do so then I suggest you follow the above advice this time around.