Hi @MSchütz,
As far as I know, this is not possible. Neither the notification settings (Settings > Notifications) nor the inbox settings (Settings > Inbox > Inboxes) offer any options here. The only option would be the general inbox access permissions (Settings > Inbox > Inboxes > Access).
Other users have already requested this from the product team: Notification control over separate conversation inboxes
I’d recommend upvoting and commenting with your context. The product team will review this if the idea gets traction and upvotes.
Best regards!