For the goal you have, the best thing to do is find something you’re passionate about and build something for it.

Ask yourself what do you love to do outside of programming? What is some problem you have that you could solve by writing a a piece of software?

You are more likely to complete a project that you are passionate about and when you speak about it in an interview your passion will show and excite the interviewer.

If there is an industry you are interested in, try to attend conventions that are relevant and go speak to the reps at the companies you are most interested in and ask questions about their products. Ask if they have any internship programs coming up and who to speak to after you’ve shown interest in their projects.

Source: an engineering manager who is not currently hiring

For backend, you won’t go wrong with something like c# .NET stack.

Personally id recommend building simple projects with both front and backend. You can still focus on backend but it will give you a feel of how a whole project hangs together. How to build APIs for the front end to call.

Whatever project you decide on building, definitely look at adding authentication and roles/scopes for APIs. It’s something I regularly see people struggle with

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.