Hola Konstantinos,
Based on what you've described, I don't think the driver store is the root cause. The strongest clue is that removing the Plug and Play device with pnputil works temporarily, but the same printer comes back after a restart. That usually means Windows still has a printer connection recorded somewhere, and the print subsystem is simply recreating the device node from that connection.
The most likely source is an old per-user or per-computer printer connection left behind from the previous print server. If these printers were originally deployed with Group Policy Preferences, there's another common possibility: the old GPP item may have created the connection without "Remove this item when it is no longer applied" enabled. Microsoft documents that Group Policy Preferences don't, by default, remove previously applied settings when a GPO is no longer applied. That would also explain why you've confirmed no current GPO is deploying the printers, but they still remain.
For your first question, pnputil /remove-device is only removing the Plug and Play device instance. It isn't necessarily the removal of the printer connection that caused Windows to create that instance. On the next restart or spooler initialization, Windows sees the surviving printer connection and enumerates the device again. The driver store may supply the driver, but it isn't what tells Windows that \oldserver\printer should exist.
For per-user printer connections, the connection is stored in that user's profile, commonly under HKEY_CURRENT_USER\Printers\Connections. Per-computer printer connections are stored separately under HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Print\Connections.
This also explains why removing the printer while signed in as a domain administrator may not work. A per-user printer connection belongs to the user who has that connection, not to whichever administrator happens to be working on the PC. If the stale printer belongs to another user's profile, removing it from the administrator's session doesn't remove that user's copy of it. For a printer connection belonging to the currently signed-in user, I'd use the supported PrintUI removal rather than deleting registry keys manually: rundll32 printui.dll,PrintUIEntry /dn /n"\oldserver\printershare" Microsoft documents /dn specifically as "Deletes a network printer connection".
If the connection was installed per-computer instead, first check the machine-level connections with rundll32 printui.dll,PrintUIEntry /ge and remove the old one with rundll32 printui.dll,PrintUIEntry /gd /n"\oldserver\printershare". Microsoft notes that /gd removes a per-computer connection and that the removal is applied when the user next logs on.
The local administrator versus domain-user difference is another strong indication that you're dealing with different connection scopes rather than a single broken driver. If the printer appears while logged on as the local administrator but not while logged on as a domain user, I'd inspect that local administrator's HKCU\Printers\Connections. Conversely, if only a particular domain user can see it, inspect it while logged on as that user, or load that user's hive and check the equivalent HKU<SID>\Printers\Connections location.
The Foxit behavior also makes sense in this scenario. Settings > Printers & scanners and an application's Print dialog don't necessarily enumerate the same objects. Settings can still expose a stale printer/device association, whereas an application may enumerate only usable print queues returned by the print subsystem. So, Foxit not showing the printer doesn't mean the Settings entry is imaginary; it suggests that what remains may be a stale device/connection object rather than a fully functioning queue.
I would not start by deleting the driver packages. Remove-PrinterDriver and pnputil /delete-driver are supported tools, but removing the driver doesn't remove the thing that is recreating the printer connection. It can also affect other printers if the new server is using the same driver package.
I'd first remove all references to the retired server at the connection level, restart the Print Spooler or reboot, and then see whether the Plug and Play entries return. If they don't, you've confirmed the root cause. If they do return, the next place I'd check is HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Print\Providers\Client Side Rendering Print Provider. Windows can retain connection information there as well; I would treat direct registry deletion as cleanup for a broken or orphaned connection, though, not the first removal method. Export the relevant key first and use PrintUI wherever possible.
Thanks,
James