Above in lines 914 and 916 I see two Create() methods with 7 uses - all of them are subject to this change. Please describe all of them in the PR description (not only Hashtable). Perhaps they should also be reflected in the tests.

It has already been described:

This PR updates the synthetic types used for tab completion and type inference to use PSCustomObject instead of PSObject as the default type name.

In other words, every instance where the synthetic type would say it's a "PSObject" has been updated to say it's a "PSCustomObject". This is in line with what we get at runtime, for example:

PS C:\> (ls | select -First 1 Name,FullName).GetType()

FullName                                    BaseType
--------                                    --------
System.Management.Automation.PSCustomObject System.Object

PS C:\>

As for the specific overload references you mention, the first one is exclusively used for Group-Object where the specified typename is Microsoft.PowerShell.Commands.GroupInfo so it's unaffected by these changes.
The second overload is used by Select-Object, Hashtable type inference, and convert expressions where the target type is psobject/pscustomobject. This is where I've made a slight fix so that: [psobject]@{Test = ls} is correctly treated as a hashtable, as the resulting object would just be a standard hashtable with an invisible psobject wrapper around it.

Everything should already be covered by existing tests that were modified for this change, or added as part of the change.

Why is the type is not PSSyntheticTypeName check removed?

I added that back in: #21184 so that it could get members for synthetic types but now that synthetic types aren't PSObject anymore, that exclusion is no longer needed.