You might want to focus on what you can do the most right now (fullstack) and change tracks later (embedded).
As a SWE in primarily python backends I can give you these ideas:
Basic CMS in Django, let’s say an eshop
Messenger-like app with FastAPI (with user management, chats, chat history, big plus would be fulltext search), this explores asynchronous events processing, this could include websockets with redis and some databases like Postgres or Maria, Mongo could work too or you could try Firebase (which is a valid trade experience but for me, experience with “real” databases/caches is more valuable).
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Also last time I heard there is always space for Java backend engineers (Spring Boot).
Focusing on fullstack you could try one of the big frameworks like Next.js (React), Nuxt (Vue) or Nest.js (backend framework) with static serving Vue/React (I might be wrong in these, I am not directly working with these tools).
Either way, personally, personal projects are cool but the main thing that counts is if you can navigate the problem space of the given field, not necessarily the absolute skill in a given framework (but definitely being a plus), for frontend it’s often about UI designs, UX etc and backends are about efficient representation of data, the processing of them and then designing something like HTTP API around them.
So choose any project you like, from websites to just processing-heavy HTTP backends (trading?), learn what problems you encounter and remember how to overcome them.