Hello Andrea Herrmann,
Minecraft might be routing through a different ecosystem. I'd recommend checking the Xbox app first rather than the Microsoft Store Library, since both Java and Bedrock editions are managed through there:
Open the Xbox app (install from the Microsoft Store if missing) > Sign in with the same Microsoft account used for the purchase > Search for Minecraft in Library and check if it shows Install.
If the Xbox app also doesn't show it, run a quick WSReset first — open Run (Win + R), type wsreset, hit Enter, wait for the Store to reopen, then check the Xbox app Library again.