It should only require you to provide source to any changes you make to Coolify itself (or code that is integrated with Coolify) if you make a public deployment of Coolify (eg. you launch a Heroku competitor).
Private (ie. accessible to employees or contractors only) deployments of Coolify shouldn't trigger the requirement. I've seen some difference of opinion as to whether giving access to a supplier triggers the requirement, giving access to a client does generally require you to provide source to them.
Code merely deployed by Coolify should not be affected in any case.
there's no difference between "private" deployment and "public" deployment. AGPL requires that if the client of the service asks for the source, you are obliged to give it to them.
So if you have a private network, but give a client/customer access to it, and they ask for the source, you will have the obligation to give it to them.
Private (ie. accessible to employees or contractors only) deployments of Coolify shouldn't trigger the requirement. I've seen some difference of opinion as to whether giving access to a supplier triggers the requirement, giving access to a client does generally require you to provide source to them.
Code merely deployed by Coolify should not be affected in any case.