So, if you have the capability, certainly go both... It will give you, at your age, the ability to build the change you want to see in the world....

Tldr; it's a lot of coursework but I've never regretted it.

I'm a TPM now, have worked on aerospace projects with small teams where it helps to be fluent in both sides of the electronics and mechanical design. I've managed multi disciplinary design optimization efforts where there is heavy intersection between code and real-world mechanical factors (writing code for my mechanical designs and writing the backbone for other contributors or translating their system to code). Being able to understand electric motor systems design end to end through the entire chain from control comms to firmware to MOSFETs, electromagnetics, and mechanics has been rewarding for me as well.

In terms of opening opportunities, small hardware startups are where I've been able to have impact, and where there is demand for someone who wants to contribute in both areas. Where I am now as TPM is a fairly limited track and PM is a bad word in some companies. At faang, it seems that software track pays better than tpm or mechanical so that is one item to note.

At larger companies it is a difficult sell for someone who wants to do both at the same time as an IC. Smaller niche companies are more likely to want someone who has the breadth and can help fill in gaps or own a whole project.

The reason I am not a pure SWE is that my passion lies in being able to hold the result in my hands at the end of the day (or week, month, year:)

I'd recommend you try out the machine shop or what is available to you if you go to an engineering college, maybe some robotics projects, mechanical engineering foundation courses, material science courses. See how you like it. I'm sure you will be successful whatever you do. If you do both it's a lot of work but I never regretted it for a second.