Podcasts app *starting* unexpectedly
Screen time lets you block apps. I would add it there first and then see if your media play F8 keyboard triggers the app.
- https://support.apple.com/guide/mac-help/set-up-screen-time-for-yourself-mchle4e2edfe/mac
- https://support.apple.com/guide/mac-help/set-time-limits-for-apps-and-websites-mchl630bc02f/mac
- https://support.apple.com/en-us/HT204436
Also watch the dock for continuity. If you’re listening on another device the Mac may be too helpful in wanting to carry on what your other device started. I use overcast on my devices so I don’t get this specific handoff.