It's easy to travel nationwide on local public transport for €9 - isn't it? Unfortunately, no. DB likes things complicated. For example, some regional trains are operated by DB Regio, while others are operated by DB Fernverkehr.
The 9-euro tick applies on the former, but not on the latter. Unfortunately, these trains are not clearly marked. You have to open the additional information in the Bahn app and read the fine print, so to speak. According to Deutsche Bahn, there is no way to prevent these trains from being displayed in the search.
Regarding the HVV semester ticket: This is valid as a 9-euro ticket throughout Germany on regional and local transport. So you don't have to buy an extra one. How the difference between the amount already paid and the 9-euro ticket will be refunded is still being clarified.