New to this party.
I am also strugling with folders on my Synology NAS en Time Machine backups to both NAS and USB drives on Catalina 10.15.5. Before 10.15.5 everything was working fine, from iMac 2017.
From various reports it seems that Apple has strengthened network security in Catalina, for instance disabling Netbios and SMB v1. This may wel explain the experiences we now have.
There is mention of a fix (or workaround) on the site Reduser.net by Bob Zelin (thanks a lot, Bob; by the way this site has more valuable knowledge and insights):
"This is how to resolve the Catalina "disconnecting" issue from NAS systems. This has nothing to do with QNAP, or Synology or any other brand. This is an Apple issue, and this is the fix.
This fix was written by Apple, but it is "hidden" and their own tech support doesn't seem to know it. (crazy - right ?).
this is as of 5/21/2020. I have verified that this works with multiple clients for the past 30 days.
On the Mac running macOS 10.15 - open terminal and type this in
nvram boot-args
you will get an error message
now, copy and paste the line below, and put this into terminal, and hit return - it will ask for your password - you will not see anything when you type in your password
sudo nvram boot-args="serverperfmode=1 $(nvram boot-args 2>/dev/null | cut -f 2-)"
now, once again, type in nvram boot-args
you will now see this -
boot-args. serverprefmode=1
reboot your Mac.
You will no longer get disconnects
Bob Zelin"
I have tried this fix an it made my Synology NAS operational again. Time machine on the NAS is working again. Albeit that my TM backup history was completely lost, because of restart of the TM trail. It may help others as well.
The lack of communication on the applied network security changes in 10.15.5 by Apple is a bit disappointing to me. I use this iMac professionally and the experienced loss of productivity en subsequent trouble shooting has taken quite some time. A little more communication and support would have been appreciated.
Hope this helps.