Ventura has frozen my external hard drives

After updating to Ventura, I plugged my two primary external hard drives into my Mac Studio to ensure they were synced only to witness their icons disappear from my desktop. Both drives now cannot mount to any of my Mac products (one Mac Studio and two iMacs - which do not run on Ventura). Both drives do, however, mount to my Windows based Surface Book, though when attempting to transfer data from either of these drives to a new and empty ExFat formatted drive, I've found that I can only transfer a relatively small amount of data at a very slow rate (I managed to transfer, for instance, roughly 400Gb over the span of nearly 48 hours), and even these transfers are not guaranteed not to move from, say 26Mb/s to zero and remain at zero for hours, leading me to consider the attempt a fail.

Yes...I acknowledge I'm an idiot because only after encountering this problem did I enroll in a cloud-based storage system. That said, these two drives house 11 years of my career as a professional photographer, and I'm in limbo without the ability to access this work. An hour-long call with Apple tech support yielded nothing but tech saying the files do exist (which I was aware of) and this is an issue known to Apple, though they've not bothered to inform users.

Does anyone know how I may be able to recover my files without filing an insurance claim? I'm not opposed to filing a claim, but I'd rather not as there are on these drives images of people who would rather no-one beyond they and I view, and I would like to respect their privacy. Any advice will be greatly appreciated.