We have created, among others, the following internal department teams in our Teams app:
Each team has their own channels for projects for which their department is the primary champion. For example, most client projects are set up as channels within 'Client Services' team, but the entire company should have access to those.
The problem we have is that most projects (channels) need to be accessible by everyone. To get around this, my boss added all staff members as a member to every team. One of the problems that creates is any @ mention of a team is going to all staff, because all staff are members of everything. @ Tech is the entire company, and @ Accounting is the entire company, which makes those useless. Ideally we would have "members" of a Team, and then internal guests of that Team who are able to browse and access its resources, but it appears guests are only for external users, and it doesn't work like that.
Is there a better approach to set up our teams/channels so that we can have company-wide access to most projects but also leverage internal department teams?
For access to Teams/Channels then you have to add everyone into the Team to get access to the channels.
One thing you could look at is do your users just need access to the files in the Teams and then give them access to the SharePoint document libraries.