It's likely not something you could automate, however using the Open URL action you could at least be taken to the sound setting(s) with the iOS URL schemes for Sound:
Sounds → (root): prefs:root=Sounds Sounds → Ringtone: prefs:root=Sounds&path=Ringtone Sounds → Text Tone: prefs:root=Sounds&path=Text_Messages Sounds → New Voicemail: prefs:root=Sounds&path=Voicemail Sounds → New Mail: prefs:root=Sounds&path=NEW_MAIL Sounds → Sent Mail: prefs:root=Sounds&path=SENT_MAIL Sounds → Calendar Alerts: prefs:root=Sounds&path=Calendar%20Alarm Sounds → Reminder Alerts: prefs:root=Sounds&path=Reminder%20Alerts Sounds → AirDrop: prefs:root=Sounds&path=AIRDROP
See this reference for the full listing.
Yes, unfortunately. Certainly not ideal for an Automation involving a Focus switch, however maybe have a second Shortcut as an addendum which would contain Open URL actions to the sounds you want to change.