I believe EXO doesn't handle anchor header properly when dealing with 'Exchange.Manage' tokens. EXO PS uses a default anchor in UPN format, while some commands like 'Set-Mailbox -Type' do not work with it. For sure it's a backend routing issue, but it's possible to override the header and make some particular commands work.
The piece of code worked for me with the latest EXO V3:
$lastConnect = (Get-ConnectionInformation)[-1]
$ctx = [Microsoft.Exchange.Management.ExoPowershellSnapin.ConnectionContextFactory]::GetAllConnectionContexts() | ? { $_.ConnectionId -eq $lastConnect.ConnectionId}
Write-Host "Default anchor: $($ctx.RoutingHintPrefix):$($ctx.RoutingHint)"
$mbx = Get-Mailbox -Identity 'example@example.com'
$ctx.RoutingHintPrefix = "MBX"
$ctx.RoutingHint = "$($mbx.ExchangeGuid)@$($lastConnect.TenantID)"
Set-Mailbox -Identity 'example@example.com' -Type Shared