I am surprised to see no honorable mention here, because a "book log" sounds a lot like a reference manager. The best free/open-source one I know of is Zotero: https://www.zotero.org

From your list of desired features above, it can do:

• tagging of items (automatically when collecting items with the browser button, manually, or a mix of both automatic tags and your own tags)
• notes as attachments to an item
• bookmarks as an URL attached to an item (and actually, most item types collected with the browser button have the URL saved by default)
• making items and their annotations public on your profile on zotero.org
• shareable format: you can export in many formats, from simple printout kind of formats (HTML) to formats fully re-importable into another instance of Zotero
• query: not sure it has all the capabilities of a relational database, but you can search based on any piece of metadata found in your items, you can build arbitrarily complex search queries, you can save searches (they will materialize in the interface as "dynamic folders" containing the search results automatically as new items added to your library match the query)

For dealing with prioritization, you would have to come up with your own system. The workflow described here uses the tag system for this (with custom tags to mark status "to read", "read", etc.): https://incenp.org/notes/2019/managing-academic-literature.html