I think a lot depends on what your goal is. Is it to better understand the methods section in the papers you are reading, or do you want to do some experimental work, or you have a job you are going after, or...

This is extremely broad and ambitious. Younger me would have said go for it as I loved to learn everything, but older me has forgotten much of the stuff that I so much loved to learn, so I moved to the camp of learning what you need.

Unfortunately I don't know too much about brain-computer interfaces, especially if it's cutting edge research.

At a high level, these are my recommendations:

The basic ideas about how circuits work is presented in any introductory book, the E&M book (Purcell) would mostly be useful for device physics and transmission lines plus other RF topics (mostly EMI, crosstalk, and other things that can go wrong). Some purists might argue on which side of the equation an inductor voltage should be, but it has zero practical effect. Also, this is a book for usually the second physics course in college, so you might have done that already and just need a refresher.

Similarly, unless you expect to be either developing novel devices, or be involved in fabricating existing devices in new nodes/conditions, you can skip anything about devices (types, structures, fabrication, materials, electron bands, doping concentrations, diffusion, drift, etc) and just the voltage/current behavior between pins should be plenty (these are covered in any introductory book). The chemistry book is mostly irrelevant for EE, although in the neuroscience case it's more applicable if we are talking about invasive electrodes (but still, probably too general and broad).

Books on integrated circuits depend a bit on whether you need to learn about some other topics that are not usually presented on their own, such as fast amplifiers, mixers, oscillators, etc with CMOS technology. I'd say though that RF/MW integrated circuits differs considerably from discrete RF/MW work, so again most likely you'll get away with treating various parts as opaque building blocks, connected by transmission lines. And I'm going to guess that for BCIs the frequencies involved are quite low, so this whole branch might be irrelevant.

Probably you'll need to learn the basics of data converters to digitize the brain signals, but again I'm not sure this warrants going through a course versus just the wikipedia page and a datasheet of a specific part you want to use. As with the other things above, courses are usually designed for people making converters, not people using them.

Signals, systems, feedback, control systems are very fundamental "mathy" engineering tools that apply to more than just EE, so probably a good tool to have in general.

I see your questions about wireless systems. Again as above. Usually these books are designed for people wanting to develop these things professionally, and if you just want to communicate wirelessly it's mostly learning the "API" that some chip has to do what you want. Not to mention the compliance nightmare to roll your own if it's beyond a handful of prototypes.

I think you get the theme. Sadly EE outside the companies making ICs has become very similar to software where you are basically plumbing black boxes together. And if you don't have a standard application, with lots of time spent on figuring out hacks to use existing parts in non-standard ways, because if you can't find the perfect part the barrier to rolling your own is much steeper than not in software.

So in a way, The Art of Electronics is very applicable. Unfortunately I think it's terrible to learn from unless you already know the stuff, and (unless it has been refreshed to the point of a major rewrite) the copy I have is extremely outdated that I never really recommend it to anyone, and I haven't opened it in a decade.

Unfortunately I don't know of such thing, but if anyone here knows a course from the Neuroscience side doing experimental work, you could see what the prerequisites for that are, and go from there.

But if you are not like me and can still learn a lot of new things without forgetting too much, go for it all and live the dream!