At the end of the day, it depends on how the app is making DNS queries.
I guess the vast majority of apps use Android’s default DNS resolver. When you’re using a VPN app like Orbot, all network traffic is supposed to be sent through it, even DNS queries when “Private DNS” is disabled. So your queries will hopefully not “leak” to your router/ISP.
However, some apps may use their own DNS resolver, possibly over TLS or HTTPS, bypassing Android’s defaults. For instance Firefox can be configured to use DoH (DNS over HTTPS). All DNS queries made by these apps will be sent to their configured resolver, which will “see” them. If these queries are not encrypted in transit (with DoT or DoH), intermediary network nodes will also be able to “see them”. In any case, there will be an information leak.
Finally a few apps are natively able to make queries through tor (by embedding a tor library), like the Tor Browser itself or Cwtch. Theses apps can connect to .onion addresses even when “Private DNS” is enabled. If you just need to access web pages over Tor, possibly with an .onion address, you can simply use the Tor Browser without having to change your “Private DNS” settings.