Recycle Bin can be enabled on a mapped network drive by defining a Known Folder in the registry. (Also a way to create custom user folders. For adding folders to This PC, though, it seems you need to create a CLSID entry instead; use Winaero Tweaker for that.)

Known folder.reg

Windows Registry Editor Version 5.00

; For folder icons, set folder to read-only and create a desktop.ini set to
; read-only|system|hidden with contents:
;   [.ShellClassInfo]
;   IconResource=C:\Path\To\Icon.ico,0

; Remember to change the guid for each known folder:
; https://www.guidgenerator.com/

; https://docs.microsoft.com/en-us/windows/win32/api/shobjidl_core/ns-shobjidl_core-knownfolder_definition
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\FolderDescriptions\{E40D77EC-D4D6-4099-9746-A81C56EA49D5}]
"Category"=dword:00000004
; The known folder name can be typed into the explorer address bar (or Run
; dialog, etc.) to navigate to the folder, e.g. "shell:Books"
"Name"="Books"
; Uncomment ParentFolder to make relative to user profile folder
; Other known folder ids: https://docs.microsoft.com/en-us/windows/win32/shell/knownfolderid#constants
;"ParentFolder"="{5E6C858F-0E22-4760-9AFE-EA3317B67173}"
"RelativePath"="S:\\Books"

; Enables recycle bin for a location that otherwise wouldn't have one (i.e. network share)
; 500,000 MB = 0007a120
[HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\BitBucket\KnownFolder\{E40D77EC-D4D6-4099-9746-A81C56EA49D5}]
"MaxCapacity"=dword:0007a120
"NukeOnDelete"=dword:00000000