There are all kinds of possibilities here, and it's hard to tell with limited information.
However, it's entirely possible that the app is consuming excess resources, throttling other parts of the system. The question is which one(s).
There is a new feature in iOS called Game Mode, which is automatically activated when certain (predominantly game-based) apps launch. They suspend certain background tasks to give more headroom (memory, CPU time, bandwidth, etc.) to the game, for a smoother game play. It could be this that's enabled with Honkai Star Rail is running.
It could also be that even without Game Mode, the app is consuming all the CPU resources, affecting other apps, or maybe it's saturating the network with updates or synch data, thus limiting the bandwidth available for the speed test.
Suffice to say, it's impossible to say from afar what the specific issue is, but if it started when you installed the game, and you don't experience the slowdowns when the game isn't running, it seems like a probable candidate.