May I add Steven Kay's Fundamentals of Statistical Signal Processing volumes to your already great textbooks recommendations.
The math behind ML are of similar difficulty yet when there are thousands of grifters promising your average front-end wevdev AI expertise in N number of videos, no one bats an eye.
Unfortunately, the barrier to research level positions is much higher than simply having the capability of going through an arbitrary list of textbooks: a number of publications in large relevant conferences or journals, e.g. ICASSP, IEEE Transactions on Wireless Communications, is what will make you an attractive candidate for them.