I'm confused by what AD considers a bridgehead server
… Commonly …
A bridgehead server is a domain controller in each site, which is used as a contact point to receive and replicate data between sites. For intersite replication, KCC designates one of the domain controllers as a bridgehead server. In case the server is down, KCC designates another one from the domain controller. When a bridgehead server receives replication updates from another site, it replicates the data to the other domain controllers within its site
The bridgehead server is a domain controller that has been either administratively assigned or automatically chosen to replicate changes collected from other domain controllers in the site to bridgehead servers in other sites. If you have the need to move a domain controller to another site you have to check if it is a preferred bridgehead server, so you must configure it to not be a preferred bridgehead server before you move the server object.
You can native get BH server information as defined here:
Note it will not show IPA’s as well.
As far as any custom module providing similar info, that module could simply be constructed an object with any additional information that the author felt was interesting. So, really not a direct comparison to what you may see via a GUI or elsewhere.
Get-ADSite -Name 'Default-First-Site-Name' | Format-List -Force
If you are using any tool that does not give you all you are after, you can simply add that property, in most cases, by using the results from one to get other as a calculated property or custom object.