If I start a project and share it with a client, does the client have to pay anything?

No, your client doesn't have to pay anything.

Initially, the invited client will be using the full version of TeamWave on trial. Once the trial period is over, their access will be limited to the projects that you have shared with them.

If they want to use the full version of TeamWave (with the ability to start their own projects) they have to upgrade, in which case they will be charged.

Note: Inviting a client or vendor to collaborate is absolutely free. You are not billed for clients/vendors that you invite.