Zeplin is great for Developer handoff and setting as source of truth for Design and Developemt. InViosion is the standard for communicating/testing design ideas and prototypes with stakeholders. Both applications offer unlimited projects. I use them on a daily basis at big enterprises and for small weekend projects.

I have been using Basecamp since 2008 to handle my client communications. I have gone through all of its three iterations.

I'd recommend Basecamp above the others because:

• It is a communication tool through and through. Looking at your description, that seems to be what you need. Zeplin is a developer handoff tool. It isn't designed to cover a more broad use case as you describe. Invision has some features that you want, but it is primarily a tool for building quick low-fidelity prototypes from website mockups. Figma is a great design tool. For the last two, communication is a secondary feature.
• It was designed by a design agency (37 Signals) for their own needs, which were quite similar to yours. (They later closed the agency to focus on Basecamp as a product full-time)
• It has flat pricing that doesn't count the number of projects, clients or team members you have. You don't have to think twice about opening another project or inviting another user. You always pay the same price.
• It can separate team and client communications. The team can talk about something without the client ever seeing it, in the same context.
• It can keep todo lists, which I think you will need anyway.
• Access control is based on projects. Every team member or client will only see the projects they are invited to. They will not even know the existence of others. (Except admins. They can see and join all projects)
• It is easy to understand and use. The design is free of clutter and easy on the eyes. Your clients (especially the tech-averse ones) will appreciate it.
• It has mobile/desktop apps with the full functionality of the web app. You won't have to wait for someone to sit down to get a quick approval.

The only real downside for me was the lack of language support in the user interface. You will be fine if your users understand some very basic written English. Some of my clients did not, so I had to walk them through it.