Use Siri to play currently selected podcast in Overcast
As of Overcast 5 (released in 2018), Siri commands are now supported. To enable, go to Overcast.app ➡️ Settings ➡️ Siri Shortcuts. Then, for example, you'll be able to say Hey Siri, Overcast play to play the currently selected podcast. (Source)
Bonus:
After Overcast is playing audio, you can use the OS-supplied Siri commands for AirPlay to send audio to another output device. Example: Hey Siri, play this in the Living Room (Source) It's annoying that you have to wait until your podcast is playing, and then speak over it to change output, but as of December 2021, Overcast does not support compound commands to both start playing a podcast and specify an output.