Yup the problem is the drive is formatted with exFAT. Sonoma has been failing to mount exFAT drives.
I had some external hard drives formatted in exFAT. Disk Utility didn't mount them...name grayed out in left column. I ended up using EaseUS software to let me into the unmounted drive so I could copy files to another drive (formatted APFS). Was software recommended on MacWorld. Cost about $100 for one month's use of software but so worth it. EaseUS did take about 10 hours to scan my 10 TB drive. I couldn't simply copy over the whole drive, or I didn't understand how to. If you copy a folder, all you get is the folder and not the contents, so I had to select individual files to copy over. Some files were corrupted, but I was able to copy all my photos and video clips.
I'm now investing in lots of cheapish external drives so I can have 3 copies on separate drives of anything that's critical to keep.