I haven't used Strapi (which looks REALLY COOL), but I've done some non-production hobby-work in NextJS, KeystoneJS, and Parse. For what you're doing - the thin stack of Strapi/Gatsby/Netlify might be enough - but if you ever get beyond basic CMS integration & content display, and need more robust data-sharing, login management, and customized usage tracking or display logic - you might need something a little more robust like Next.js, Keystone, and/or a backend like Parse.
For the "thin-stack" model - you'd likely need to generate a common config/ENV file that sits at the root of each of your sites. These should likely contain generation / CMS access keys (unique to each site) to request data for each deploy build to collect page/site content from the (presumably centralized) CMS.
If you're looking at high-volume of sites, with limited staff, you're going to want to automate access generation and deployment at some point. You might want to look into some orchestration tools to help with some of the deploy / generation / API / CMS key stuff. I've used Azure DevOps in production, and Vercel has an interesting approach I use for hobby/prototype work, and I think Heroku might have some options as well.
Good luck! Hope you kill it!