I like the Practical Antenna Handbook even better.
It is the defacto 'just above layman' text on the subject. It gets somewhat dense on the math in places, but you can skim through that without losing the most important bits.
Welcome! We have a few articles on our wiki to get you started, since you're asking about the Tech exam I'll assume you're american so I'll point you towards the Getting Started, USA article.
The ARRL, has a handful of books on the subject, which are also available on Amazon. Another one I'd like to recommend would be the Practical Antenna Handbook which I find a lot easier to read.
/u/taxilian here runs hamstudy.org which is great for gauging your preparedness.
Now if you're into computing you should also check out Software Defined Radio and gnuradio for some very powerful tools in the RF space. You can also use SDR# (windows) or GQRX (linux) to view broad swathes of the RF spectrum in real time. An excellent overview of what you can do with this technology can be found here
Carr’s Practical Antenna Handbook is excellent. Good combo of theory plus (as the name suggests) practical design tips.
Great questions and finding the answers and figuring it all out is the best part of the hobby for me. Literally any copy of the ARRL Antenna Book will help with most of these, but it is not made to be read through but rather to use the index and cover a topic or a particular antenna at a sitting.
I am a book collector and spend a great deal of books in any area of interest I have and have a stack of books on antenna theory and a recent copy of the ARRL Antenna book along with O4UN's Low Band DXing (also excellent resource). However, on a whim, I got a copy of the book below and it was so "just what the doctor ordered" for where I was in my understanding, that I read it from cover to cover. I honestly feel I am a better ham for it.
https://www.amazon.com/Practical-Antenna-Handbook-Joseph-Carr/dp/0071639586
You've got a lot of good advice in this post that pretty much covers what I was gonna say. I can relate to you when you say that you really understand the subject by working through all the details and the math. However, I've found that when it's time to actually put theory to practice, a lot of times you can't do it directly because the problem at hand is way too complex. And like you said, that approach takes a very long time. So, a compromise I've made is that I just start doing the project, and then learn the theory in parallel. That way, you sort of start to get both the intuition and the solid foundations behind what you're trying to work on.
Also, a practical book I'd recommend is Practical Antenna Handbook. I've skimmed through it and it seems like a really good book to get a feeling for working with antennas. It's definitely on my to-read list. If you really want the nitty-gritty of antenna theory, I've heard good things about Balanis and Kraus.