0. It's not you, it's the job market and economic cycle. Many companies aren't hiring much at the moment because of economic uncertainty and unrealistic enthusiasm about AI-fueled automation. But the good (?) news is they are trying to cut costs by laying off senior people and hiring junior people like you. Keep applying.
1. You could lean into the EE side of things. Analog and digital design are still needed as we move into the era of RISC-V, robotics, AR/VR, self-driving cars, etc. You likely have a decent project portfolio already from your coursework. Also power engineering and efficiency are important at all scales.
2. An MEng from MIT (or another good school/program) would probably be interesting, challenging and fun, and you'd pick up some additional skills. It would also enable you to apply for internships, which can be easier to get than full-time/"permanent" positions, and can lead to the latter. Try to get teaching or research assistantships to avoid or reduce debt (even if it takes longer, it's worth it.) And you could potentially do a Ph.D. later on if it turns out that you like research.
3. Economic downturns can be good times to start companies because there are more people on the job market. Also you may be able to get good deals on office and lab space and equipment if you need it.
4. If you can't join a startup as a co-founder, you may be able to join as staff. Make sure they pay you a salary though.
5. Look into temporary or contract work, or any job you can get that pays money, ideally enough for food and rent in a starving student type shared residence. Then keep looking for something better.