Issues with Set-LMWebsiteGroup

I haven't used this module but quick look at the code seems to be able to report some debug info although I'm not sure exactly how to turn it on. Try adding "-debug" to the Set-LMWebsiteGroup command or running "$DebugPreference = 'Continue'" before the line. If you get more details from that let us know what it says.

PS C:\WINDOWS\system32> set-lmwebsitegroup -Verbose -Name 'CNVPABACUSS252/Servicing/Loan' -ParentGroupName 'Production/Internal/DevOps/Individual Nodes/Abacus Sync'
VERBOSE: GET https://caliberhomeloans.logicmonitor.com/santaba/rest/website/groups?filter=name:"CNVPABACUSS252/Servicing/Loan"&size=1000&offset=0&sort=+id with 0-byte payload
VERBOSE: received 74-byte response of content type application/json

PS C:\WINDOWS\system32> set-lmwebsitegroup -debug -Name 'CNVPABACUSS252/Servicing/Loan' -ParentGroupName 'Production/Internal/DevOps/Individual Nodes/Abacus Sync'
DEBUG: Invoked Command: Get-LMWebsiteGroup
DEBUG: Bound Parameters: [Name:CNVPABACUSS252/Servicing/Loan]
DEBUG: Invoked URL: https://caliberhomeloans.logicmonitor.com/santaba/rest/website/groups?filter=name:"CNVPABACUSS252/Servicing/Loan"&size=1000&offset=0&sort=+id
DEBUG: Request Headers: [Authorization:LMv1 2vPfj2uZ6qAM4rnrygFV...] [Content-Type:application/json] [X-Version:3]

That's the debug I got using one of the many ways to try and update the grouping.

Hmm, that looks somewhat incomplete as it's only showing the GET request and not the PATCH request that it does later. I'm not in a position to test out this module myself. You may need to reach out to the developer of the module.