Team Computers assigned to a group are considered Shared Computers, meaning multiple team members may have access to them. For anyone with access the computer will show in the Computers tab in Parsec and they can connect to it as if it was their own. When users are connected an icon shows in the corner. Multiple users can connect at the same time. You can restrict multiple people from connecting at the same time, however, by using the advanced setting that sets the max connections. You can set this to 1, and only one person will be able to connect at a time.
Please read the documentation about Team Computers.
Shared computers can only be assigned to one group, but they can still be shared among multiple groups. This happens through connections between groups.
When you assign a computer to a group you don't give access to that group, instead you make the computer part of the group. This means the group's members can only connect to the computer if the group has "Allow Connections Within Group" enabled. Members of other groups can also connect to the computer if their group has an outbound connection to the computer's group. These can be configured when editing the group on the Groups & Members page.
Group connections control what users are allowed to connect to what other users, and what shared machines user can connect to. Even if a user has group permission to connect to another user they can only do so if the target user shares a link or befriends the user that wants to connect. If a user has group permission to connect to a shared computer they can always connect.
The Design group has "Allow Connections Within Group" enabled. If you assign a computer to the Design group all members of that group will be able to connect to the computer. Members of the Design group are also allowed to connect to each others computers, but only through share links or friendships and with explicit approval from the computer's owner.
The Engineering group has permission to connect to the Design group. All members of the Engineering group will also be able to connect to the computer. They are also allowed to connect to computers belonging to Design group users, but again only through share links or friendships.
QA shares computers. They should all be able to connect to these shared computers but not to each other. To accomplish this the QA group has "Allow Connections Within Group" disabled but it has an outgoing connection to the QA Computers group. This is a group that only contains shared computers.