No, it has not always done this. App-based Focus triggers are designed to stay active as long as the app is running or open in an active session, but locking the screen or sending an audio app to pure background processing has introduced intermittent bugs in recent point releases like iPadOS 26.5.
Try this
Use a Manual Toggle or Control Center: Instead of an app trigger, turn on Do Not Disturb manually or via a Home Screen widget before locking your screen.
Use the Shortcuts App: Build a custom automation via the shortcuts app that turns on Do Not Disturb when the Podcast app opens, but avoid relying on the automatic exit state if it misbehaves on lock.
Toggle Share Across Devices: Go to Settings > Focus, toggle off Share Across Devices, restart the iPad, and turn it back on to clear out syncing glitches.