I am trying to set a report filter for project owner ID is $$USER.ID but I also want to filter this report to only users from a particular team. It's not their home team ID but another team they belong to. Can anyone help me with that text mode?

I'm not sure I understand what you're trying to do. If you filter by Project Owner = $$USER.ID, whoever opens that report is only going to see projects they are the owner of. They aren't going to see any other user's projects, no matter what team(s) they might belong to.

If you only want members of this team to be able to view the report, you can share it with only them. But each individual user will only be able to see their own projects, not the rest of the team's projects.