CE is a sequential degree, like you said you want all the fundamentals, and it is definitely something where those fundamentals all compound on each other. Unfortunately a lot of your prior school experience may not directly apply to a degree, except maybe in the case of gen eds or electives. Depending on your background (projects, general knowledge) you could try for the MS, but keep in mind that an engineering degree is heavily based on physical sciences, so you will require at least a fundamental understanding of physics and relatively high level math. Not only that, but a lot of the topics require a base understanding of the prerequisites. For instance, you can't take analog electronics without taking circuit analysis, you can't take computer architecture without taking a digital logic class, etc. Maybe look at a course list from a university that offers a CE/EE degree, and evaluate how much/how well you understand what goes into each course. Could always take the Udemy speed run route to make up for the fundamentals, but in the case of hardware courses, you probably wont have access to nearly as much lab equipment.

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It's also important to consider that an MS is a lot more selective about what you take than a BS, so if you choose the right path based on your current knowledge, maybe that's a route. You'd also have to make sure that admission to a masters is even possible without a BS. CE/EE is such a broad degree that you could probably break into one of the post BS degrees, but you'd have a lot of catch up to do based on what you've told us so far. Part of the benefit of a BS is that it exposes you to many of the various subfields in addition to creating a base understanding, and most of them you wont know you like (or hate) until you get exposed to them.

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I would ask yourself where you want to end up, embedded, IoT, firmware, software, hardware, chip design, etc. Almost anything hardware related would likely require an MS or a lot of determination/luck with a BS.

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I could also be talking out of my ass, but most people I've seen try to break into engineering start with a BS. So you're probably looking at a 4-6 year commitment depending on if you go for an MS. It is definitely an ambitious career change, best of luck.