Thank you. Your comments clarified a few things. I added useApiV3 = $True to the body above, and removed the incorrect use of endpointUrl. The big mistake in the above was Register-PSRepository - I needed to update Microsoft.PowerShell.PSResourceGet to the latest version, and use Register-PSResourceRepository -Name $feed.ShortName -Uri $endpointUrl -ApiVersion 'V3' -Trusted -passthru, where endpointUrl was http://<hostname>:50000/nuget/$feed.ShortName/
Problem solved, thanks again!

I'm trying to use ProGet as an internal package repository for my organization. I want to use it to test the packaging and delivery of modules in a variety of packaging formats and feed protocols
I want to push PowerShell modules/packages that support Prerelease / Released kinds and Production / QualityAssurance kinds of packages.
I want to push to feeds with protocols conforming to NuGet, PSResourceGet, and Chocolatey.

I use a PowerShell script to create a set of HTTP (not HTTPS) feed endpoints for these 12 combinations, using the V3 protocol

I use this command:
$feedCreationResults = Invoke-RestMethod -Uri $feedAdministrationUri -Method Post -Headers $headers -Body ($body | ConvertTo-Json -Depth 3) -ContentType 'application/json'

where:

$feedAdministrationUri = "http://utat022:50000/api/management/feeds/create"
$headers  = @{ 'X-ApiKey' = $adminApiKey }
$body = @{
      name                      = 'IntRelPSProdPushFeed'
      alternateNames            = @()
      feedType                  = 'powershell'
      active                    = $true
      cacheConnectors           = $true
      symbolServerEnabled       = $false
      stripSymbols              = $false
      stripSource               = $false
      endpointUrl               = 'http://utat022:50000/Released/Production/powershell/v3/index.json' (the word powershell is also replaced by 'nuget' and 'chocolatey' for those feed endpoints)
      connectors                = @()
      retentionRules            = @()
      variables                 = @{}
      canPublish                = $true
      packageStatisticsEnabled  = $false
      restrictPackageStatistics = $false
      deploymentRecordsEnabled  = $true
      usageRecordsEnabled       = $true
      vulnerabilitiesEnabled    = $true
      licensesEnabled           = $true
      useWithProjects           = $true
    }

Using the ProGet dashboard, I can see that all 12 feeds are being created with their appropriate feed names, but...

When I inspect the feed at
'http://localhost:50000/feeds/IntRelPSRProdPushFeed'
it says the feed API endpoint URL is
http://localhost:50000/nuget/IntRelPSRProdPushFeed/

Regardless of the ProGet feed type I use in my endpointURL (nuget, powershell, chocolatey), the feed endpoint type in ProGet is always nuget, the feed endpoint host is always 'localhost', not 'utat022', and the subpaths are missing. The "supported API" is v2 for powershell and chocolatey feeds, and "v2 and v3" only for nuget feeds

Furthermore, attempting the command
Register-PSRepository -Name 'IntRelPSRProdPushFeed' -SourceLocation 'http://utat022:50000/Released/Production/powershell/v3/index.json'
results in the message

Register-PSRepository: The specified Uri 'http://utat022:50000/Released/Production/powershell/v3/index.json' for parameter 'SourceLocation' is an invalid Web Uri. Please ensure that it meets the Web Uri requirements.

Could somebody point out what I'm doing wrong?