You neglected to provide some very important details such as the file system on your Seagate drive and whether you are using any proprietary third party software to manage that drive, and the exact model of that drive (plus if an SSD or Hard Drive, cable type & connection). In addition, is the physical drive seen by Disk Utility? Within Disk Utility you may need to click "View" and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility.
And was this a minor Sonoma update patch, or a major OS upgrade from Ventura to Sonoma? I believe you mean the former, but it is not entirely clear.
If you are using third party software to manage the drive, then make sure to check for any software updates to that software. If you are up to date, then contact the developer of that software for assistance.
Are you using any anti-virus software, cleaning/optimizer apps, or third party security software? If so, this may be the problem.....uninstall them by following their developers' instructions.
Make sure to disconnect all other external devices in case one of them is causing a problem.
Also make sure to connect the Seagate drive directly to the computer. If this is how you do have it connected, then try connecting it to a USB3 hub since I've seen some reports on this forum where this allows some external drives to work properly.
If the physical drive is seen by Disk Utility, then run First Aid on it (see my earlier instructions in the first paragraph).
Since you are freaking out here, I'm assuming you don't have any backups of the data stored on this Seagate drive? Why? If the data is so important don't you have backups? The more important the data, the more backup copies of the data you should have and usually using two different backup methods as well. Apple includes Time Machine with each copy of macOS to make backups easy.
If you have no backups, then you can try using data recovery software such as Disk Drill, or Stellar Data Recovery (I've never used either one). Most data recovery apps allow you to scan the drive for free in order to see what items it can discover, but will require you to purchase the app if you wish to recover those files. Keep in mind that depending on the issue with your external drive.....you may lose file names & folder structures if an extended/deep scan is necessary to recover the files.
There is also a possibility the Seagate drive is worn out or failing, or you may have a cable or port issue. Yes, I realize this occurred apparently as a result of an OS update, but I have seen such coincidences in the past.
You can also try booting into Safe Mode, but if you are using third party software to manage the external drive, then Safe Mode is not an option.
FYI, most people have no issue with minor macOS update patches as long as they don't install junk software, or software that is known to be unstable because the developer doesn't keep their software up to date or follow Apple's recommendations for developing apps. With a major OS upgrade from 13.x to 14.x, then yes....there can be issues so it is critical that a user does their own research & testing prior to upgrading their critical systems (having a spare test system & proper backups is part of that process as well).
