I have been invited to Open as App by a different company. Do I need a separate Open as App account in order to share my own "Excel-Apps" with my team?
No. You can belong to multiple teams and simultanieously manage your own team in one account.
Create and manage your team in the Open as App portal. Detailed instructions for user management at Open as App can be found here: Team, users, groups and guests | Manage user access rights
At the settings you can see all Team memberships in the app player.