No longer able to access shared files on network computer

You've toggled off Wifi & then back on on both ends?

Are you running any Anti-virus or Cleaning Apps? VPN?

Find the IP of the other Mac in Network Pref Pane for that Interface, then on this Mac>Finder>Go>Connect to Server, try entering...

smb://ip/of.other.mac

Oh, you do have SMB Sharing enabled as Apple dropped AFP support?

UPDATE:

I think I found a workaround, but I still don't quite understand what is going on. Here's what I found:

1. When I was trying to figure out what was happening, I did what others have suggested, which is to erase any saved passwords on the MacBook Pro for the smb login to the backup server (connected to the iMac) in KeyChain Access. However, whenever I would connect to the server again (using cmd-K), it would somehow reconnect automatically using the iCloud username. I.e., it wouldn't ask me for a username and password. Also, even if I disconnect from the server and then try the "Connect As" button through the Finder, nothing would happen.
2. The iCloud username on the MacBook Pro is not a user on the iMac and I suspected that it was this that was causing the permission error. I had tried everything I could think of and everything I was able to find online to get the MacBook Pro to connect to the backup server using a different username that already existed on the iMac (smb://username@shared_folder....), but I kept getting the same error. I even created a new "Sharing Only" username on the iMac and tried using that to connect to the backup server from the MacBook Pro, but I ket getting the same error.
3. So, I decided to create another "Sharing Only" user on the iMac with the same iCloud username from the MacBook Pro and connected again to the backup server through cmd-K.
4. Sure enough, that solved the permission issue and now my TimeMachine backup is working again.

I still don't know why the MacBook Pro is insisting on only using the iCloud username to connect to the backup server, but I am happy that at least it is working (for now).

If I have them automatically get mounted by means of having the volume be one of the startup items (in control panel->users) then it looks like a greyish blue drive with little people holding hands. BUTTT if I mount one manually, myself, by going to Go -> Network ... the icon looks brighter blue and has the wifi symbol on it.

https://apple.stackexchange.com/questions/110771/why-do-shared-network-drives-mounted-on-my-mac-have-icons-vary-depending-on-ho

If they in fact do show up on the Desktop, then create a new Folder maybe named Shares on/in the Desktop, drag all those Shares shown on the Desktop to that Folder, drag that Folder to the right side of the Dock between Applications & Trash, this should give you a popup menu to select from.:-)

Mount that Share once, then once they show up on the Desktop, drag that Icon to the right side of the Dock between Applications & Trash. You now have a Dynamic Mount, a quick click on the Icon in the Dock will connect you.

On the multiple Shortcuts...

Mount them all, when show up on the Desktop, then create a new Folder maybe named Shares on/in the Desktop, drag all those Shares shown on the Desktop to that Folder, (you can even rename them once there, if you wish), drag that Folder to the right side of the Dock between Applications & Trash, this should give you a popup menu to select from.:-)

To automount them, drag those Aliases to the Accounts Pref Pane's Login Items Window.

I'm having the exact same issue. Shared external USB drive connected to a 27" iMac and trying to connect to it from a MBP all on the same home WiFi. The MBP uses the shared drive for Time Machine backup and it has been working for a long time, even after upgrading both computers to Catalina. The only thing that has changed is that we upgraded our FiOS router and instead of changing the SSID and password on ALL the devices in the house, I changed the SSID and password on the router to match the old router.

In searching for answers to this issue, I came across someone that said that they realized that their 2 computers were using 2 different frequencies to connect to the router (i.e., 2.4 and 5.0 GHz) and that switching to the same frequency fixed it. Since our new router automatically switches between the 2 frequencies, I thought this might be the issue. However, I reconfigured the router and disabled the 5.0 frequencies, but I was still unable to mount the shared drive from the MBP. I still get the "You do not have permission to access this server" error. I've tried all of the other suggestions I could find, but still no luck. I'll update if I find a fix for this.

What Folders are setup in sharing, can the Drobo be added there?

Only thing I can think about Wifi is it could be really slow opening a Drive/Folder with tons of icons in it.

Good work, thanks for the report. :)