I've had this problem with an external G-Drive Mobile Pro Thunder Bolt 3 (WD/HGST) SSD (connected to powered Thunder Bolt dock) since the upgrade to Big Sur, and while I do think Big Sur kicked off the issue, I'm not convinced it is root cause. I rolled back to Catalina (a state in which the SSD worked perfectly), and it still disconnected... Apple engineers when through my 2018 Mac mini and couldn't find any cause. They say it isn't the Mac, WD/HGST says it's not the drive. They both can't be right... The consumer gets caught in the middle as usual.
I have to say that both Apple and WD/HGST support have been very responsive (actually I did have to chase down Apple engineering for the results of their root cause analysis). I'm on my 5th replacement drive and this one is brand new, kudos to WD/HGST support for their effort.
I've done a lot of troubleshooting and reconfiguration (including power), and as of today it appears to be working fine (it hasn't disconnected in 3 days), but I've seen this behavior before so, it still may...
It is possible that Big Sur did something to tweak power management at the system level. Power seems to be the most consistent thing that pops throughout all of the posts I've read since November 2020. It is a bus powered device, so I think it makes the most sense at this point. Mac mini doesn't have a battery, so I set everything to stay on, but when I've done that, it still disconnected... I've connected it directly to a TB3 port, the TB3 dock, and daisy chained off of a TB3 drive bay with the same behavior per each connection. The only difference is frequency of the disconnects. Recently, when connected to a powered device like the dock, it was disconnecting once per day-ish (vice 100 times per day). I did nothing, and no disconnects for the last 3 days. I'm going to set up a backup routine to keep the drive active for the next week or so and see what happens.
If no disconnects happen in the next week maybe 2, I'll feel much better about it.