keeping updated your custom css (in Calibre viewer or in markdown-viewer browser extension)

You can link within the css (in Calibre it is within the file "viewer-webengine.json", in markdown-viewer browser extension is the css file you yourself have chosen) your external css file, with something like
 @import url(http://localhost/path-to-your-css-file/your-css-file.css)
Provided you have a apache/php server in localhost, of course.