As far as I understand it there's no legal precedent, so we're not completely sure. Some say calling an api means it's part of your application, meaning you need to open source your app. Some say that that's not the case. I think this unknown is why the license is banned in some companies.
I think what matters more is how the creators of the software intend the license. In case of Lago it's clear they want you to use it this way, and AGPL is only really meant to restrict businesses that want to fork it and start a proprietary billing service.
That's on point.
A "proprietary billing service", or a service that includes billing in the value proposition in general: whether you're a vertical SaaS, an accountingtech, or a payment processor.
I think what matters more is how the creators of the software intend the license. In case of Lago it's clear they want you to use it this way, and AGPL is only really meant to restrict businesses that want to fork it and start a proprietary billing service.