This type of problem has been reported at least once: "New device with each app startup"
However, my case is not exactly the same.
I'm running client version 120.4.4598 on Debain 10.9, using KDE Plasma desktop.
There is some sort of hardware issue (working as a separate issue) that causes a hard lock up and I have to reset. When Dropbox restarts after reboot and login, it wants me to add the "new" computer to my list of linked devices, even though the "new" entry appears to me to be identical to the original.
Today, I decided to enable 2-factor authentication. On completion, Dropbox was logged out and when I hovered my mouse cursor over the Dropbox icon, it said "starting". When I finished the 2-factor identification, I again got a "new" linked computer in the list and hovering the cursor shows the message "up to date".
I tried stopping Dropbox using the "Quit" menu item from the icon and then manually restarted it. No problem this way.
I even tried killing the background process with signal 9 and restarting. Again, no problem restarting.
This is not a major issue, so long as I'm able to get to my Dropbox account in the browser and remove extra linked devices, but the client really should be able to figure out that there is an existing link and "reuse" it.
In general, this shouldn't occur since the computer should be seen as the same device after a normal reboot.
However, if you're experiencing hardware issues, there could be something else which is breaking the link to Dropbox. It could be changing the name of the device to a temporary name and then back to the original, or preventing the Dropbox app from permanence for its settings, or literally wiping the connection to Dropbox by resetting its settings each time it reboots.
I'd recommend checking your system to see if any of these might be a factor in what you're experiencing.
OK, but I have no idea about changes like you mention. I use the environment with minimal, if any, system settings changes. And though I have hardware issues, with the hard lock up, they are fairly infrequent. I do keep my system updated on a regular basis, so I suppose something there might have caused a change?
As for figuring out what might be changing, under the hood, I would need to know where to look, under the hood. I have no idea what files are used by Dropbox or where they are located. If you could supply some info on what to check, I can set up some monitoring to let me know if anything changes between boots, etc.