Playback volume from the Apple Watch speaker is controlled at the system level - not per app. If you can adjust the volume in one of Apple apps, it should also control the playback volume across all apps including Just Press Record. For example, make a recording in Apple's Voice Memos app on your Apple Watch. Use the Digital Crown to raise the volume in Voice Memos as it plays. Now return to Just Press Record and you should find the playback volume remains raised.