There's an open source, self-hosted clone of BearBlog, called PolarBearBlog [0], that builds a docker image and run it on Google Cloud Run. It uses Google Cloud Storage to manage a single JSON file for the whole blog contents (yes all your blog posts are in a single json file, which probably will start to show issues when you have hundreds of posts, but then again it's just markdown text so maybe that won't be a big issue anyways), and you only need to redeploy it if you made code change or system level config changes, which really is really more convenient than the whole static approach.
I made a fork of PolarBearBlog to add some of the features I care about, like cactus comment integration and rending full posts in the RSS feed. [1]
[0]: As far as I could tell PolarBearBlog has no affiliation with BearBlog, but it did get a mention in BearBlog's README: https://github.com/HermanMartinus/bearblog/blob/master/READM...