Found some partial workarounds, until such time as Piriform fixes this (And big parts of Chrome cleaning seem to be busted).
First, Add a key to CCleaner.ini:
CustomLocation1=CHROME|C:\Users\{YOUR FOLDER HERE}\AppData\Local\URBrowser\User Data\Default
It must be expanded because this ini file appears not to parse things like %LocalAppData%.
This tells CCleaner to treat the UR Browser as any other Chromium-based browser. But, alas, it is still not shown and is processed simultaneously with Google Chrome and Vivaldi.
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To get around that:
Uncheck the operations that you wish to apply to only some of the 3 browsers (EG: Clear history, clear browser session, etc.).
Then add keys to Winapp2.ini to add-back in such cleaning for each browser separately.
Here is the relevant winapp2.ini section that I use:
;--- Break out key Chromium browser sections separately and place the entries in the Chrome section.
;--- Internet History -----------------------------------------------------------------------------------------------
[Internet History Vivaldi*]
LangSecRef=3029
; This next puts the entry in the right place, but overwrites the title!
;LangRef=3162
;ID=2014 ; No apparent effect
Detect1=HKCU\Software\Vivaldi
Default=False
FileKey1=%LocalAppData%\Vivaldi\User Data\*|Current Tabs
FileKey2=%LocalAppData%\Vivaldi\User Data\*|History Provider Cache
FileKey3=%LocalAppData%\Vivaldi\User Data\*|Last Tabs
FileKey4=%LocalAppData%\Vivaldi\User Data\*|Network Action Predictor
FileKey5=%LocalAppData%\Vivaldi\User Data\*|Top Sites
FileKey6=%LocalAppData%\Vivaldi\User Data\*|Visited Links
FileKey7=%LocalAppData%\Vivaldi\User Data\*\JumpListIcons|*.*
FileKey8=%LocalAppData%\Vivaldi\User Data\*\JumpListIconsOld|*.*
[Internet History UR Browser*]
LangSecRef=3029
Detect1=HKCU\Software\URBrowser
Default=False
FileKey1=%LocalAppData%\URBrowser\User Data\*|Current Tabs
FileKey2=%LocalAppData%\URBrowser\User Data\*|History Provider Cache
FileKey3=%LocalAppData%\URBrowser\User Data\*|Last Tabs
FileKey4=%LocalAppData%\URBrowser\User Data\*|Network Action Predictor
FileKey5=%LocalAppData%\URBrowser\User Data\*|Top Sites
FileKey6=%LocalAppData%\URBrowser\User Data\*|Visited Links
FileKey7=%LocalAppData%\URBrowser\User Data\*\JumpListIcons|*.*
FileKey8=%LocalAppData%\URBrowser\User Data\*\JumpListIconsOld|*.*
[Internet History Google Chrome only*]
LangSecRef=3029
Detect1=HKCU\Software\Google\Chrome
Default=True
FileKey1=%LocalAppData%\Google\Chrome\User Data\*|Current Tabs
FileKey2=%LocalAppData%\Google\Chrome\User Data\*|History Provider Cache
FileKey3=%LocalAppData%\Google\Chrome\User Data\*|Last Tabs
FileKey4=%LocalAppData%\Google\Chrome\User Data\*|Network Action Predictor
FileKey5=%LocalAppData%\Google\Chrome\User Data\*|Top Sites
FileKey6=%LocalAppData%\Google\Chrome\User Data\*|Visited Links
FileKey7=%LocalAppData%\Google\Chrome\User Data\*\JumpListIcons|*.*
FileKey8=%LocalAppData%\Google\Chrome\User Data\*\JumpListIconsOld|*.*
;--- Browser Session ------------------------------------------------------------------------------------------------
[Session Vivaldi*]
LangSecRef=3029
Detect1=HKCU\Software\Vivaldi
Default=False
FileKey1=%LocalAppData%\Vivaldi\User Data\*|Current Session
FileKey2=%LocalAppData%\Vivaldi\User Data\*|Last Session
FileKey3=%LocalAppData%\Vivaldi\User Data\*\Extension State|*.*
FileKey4=%LocalAppData%\Vivaldi\User Data\*\Session Storage|*.*
[Session UR Browser*]
LangSecRef=3029
Detect1=HKCU\Software\URBrowser
Default=False
FileKey1=%LocalAppData%\URBrowser\User Data\*|Current Session
FileKey2=%LocalAppData%\URBrowser\User Data\*|Last Session
FileKey3=%LocalAppData%\URBrowser\User Data\*\Extension State|*.*
FileKey4=%LocalAppData%\URBrowser\User Data\*\Session Storage|*.*
[Session Google Chrome only*]
LangSecRef=3029
Detect1=HKCU\Software\Google\Chrome
Default=True
FileKey1=%LocalAppData%\Google\Chrome\User Data\*|Current Session
FileKey2=%LocalAppData%\Google\Chrome\User Data\*|Last Session
FileKey3=%LocalAppData%\Google\Chrome\User Data\*\Extension State|*.*
FileKey4=%LocalAppData%\Google\Chrome\User Data\*\Session Storage|*.*
;--- Download History -----------------------------------------------------------------------------------------------
; APPEARS NOT TO WORK FOR ANY CHROMIUM BASED BROWSER!
;--- Saved Form Information -----------------------------------------------------------------------------------------
; APPEARS NOT TO WORK FOR ANY CHROMIUM BASED BROWSER!
;--- Saved Passwords ------------------------------------------------------------------------------------------------
[Saved Passwords Vivaldi*]
LangSecRef=3029
Detect1=HKCU\Software\Vivaldi
Default=False
FileKey1=%LocalAppData%\Vivaldi\User Data\*|Login Data
[Saved Passwords UR Browser*]
LangSecRef=3029
Detect1=HKCU\Software\URBrowser
Default=False
FileKey1=%LocalAppData%\URBrowser\User Data\*|Login Data
[Saved Passwords Google Chrome only*]
LangSecRef=3029
Detect1=HKCU\Software\Google\Chrome
Default=False
FileKey1=%LocalAppData%\Google\Chrome\User Data\*|Login Data