9 Euro Ticket for Black Forest and Berchtesgaden

The 9 EUR ticket is not valid for buses, except for replacement buses where the rail line is closed for repairs. It is only good for regional trains, not IC, ICE, or EC trains.
If you stay at a qualifying hotel in the Black Forest region, you will get a guest card that does allow you to use the regional trains and buses in the region for free.

Sam, that information is incorrect.
The 9€ ticket is valid all over Germany on all forms of public transportation, including buses and trams. Just not ICE and IC, EC trains.
https://www.rmv.de/c/fileadmin/documents/PDFs/_RMV_DE/Fahrkarten/9-Euro/186_22_004_9-Euro-Ticket_Baukasten_OnePager_ENG.pdf

I stand corrected, but checked back to see the following fine print in the DB 9-Euro-Ticket section. Note last line.

Where can I use the 9-Euro-Ticket?
The 9-Euro-Ticket is valid on all public transport services in Germany. You can use it on any local/regional route and make as many journeys as you like.
This is true regardless of which transport service provider, transport association or tariff is indicated on the ticket. A 9-Euro-Ticket purchased in Munich, for example, can also be used for journeys in Frankfurt and the surrounding area.

The ticket is not valid on long-distance trains (e.g. IC, EC or ICE) or long-distance buses. However, if your regional train is more than 20 minutes late at the arrival point, you can take a long-distance train if you buy a long-distance ticket beforehand. When you have completed your journey, the passenger rights service centre (Servicecenter Fahrgastrechte) will reimburse you for this long-distance ticket on request. For exceptions, please check the area of validity in the Conditions of Carriage at bahn.de/agb.

Please also check with local bus companies whether the ticket is recognised.

Please also check with local bus companies whether the ticket is
recognised.

This is genuinely not necessary in nearly all cases. The 9-Euro-Ticket is valid on local busses, with a few extremely narrow exceptions, like tourist coaches serving special locations. Normal local busses are certainly included (and, as bus drivers in DE generally ask to see tickets when one boards, this should all be fairly transparent/easy for tourists).

The 9-Euro-Ticket is valid on local busses

True, but ...

... unfortunately, the DB website /app misleadingly very often shows "partial fare" for connections involving a bus. This is due to the fact that, as a result of the hasty introduction of the 9-euro ticket, there were no acceptance confirmations from the bus operators, and without these, DB does not show the validity of the ticket on buses (to avoid recourse claims). Moral: With regard to the buses, DB is playing dumb, but the €9 ticket is valid on them.

Yes, yes. Agreed. The main DB app is not good at showing this.

But just (from my perspective): tourists should proceed with the belief that normal regional busses are covered, and not feel that they need to chase down the website of the RVF (in the case of parts of the Black Forest, for example) to see if their busses are included. They are.

Does the 9 euro ticket also apply to inter-city public transport?

It is valid on all public transportation that is regional. Not ICE, not IC, not EC. Everything else, yes.