Have you tried Netlify?
No - tell me about it!
Its made specifically for hosting static sites, but it can have forms 😮. I hear it also makes working with AWS lamda functions a bit easier, although I haven't tried that yet.
You can use Github, Gitlab or Bitbucket and it will update the site with every merge.
I've personally only used it for single-page HTML websites, but I hear it integrates nicely with static site generators.
And it has a generous free tier :)
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