Yes, htmz is a great project! The core idea is similar, but htmz is intentionally more minimal (it's literally 166 bytes). µJS covers more ground: patch mode, SSE, DOM morphing, View Transitions, prefetch, polling, full HTTP verb support.
You should be able to push to history using history.pushState(…) after loading a new page. There are probably more details needed around popState to handle back and forward navigation. I’m sure Claude will be able to assist here, but maybe too much complexity when smaller libraries could manage history state.