I play and sing Jazz standards all the time. I never used a ukulele specific book, but I did explore some.
The music is more complex than your standard folk music but once you understand the roadmap and the rhythm. it's fairly easy. Most of the songs follow some variation of 136251 chord progression, normally written with Roman numerals. Any jazz standard will almost always resolve with the II V I pattern. When I was blindly trying to learn this I downloaded some tutorials from Doctor Uke. He has a few songs with the above chord progression and he puts them in every single key. Starting with 5 foot 2. At first it was daunting. but eventually you realize the circle of fifths follow the same pattern so when you go to the next key you're only adding one more chord.
https://www.doctoruke.com/theory.html
Playing with other people who know the genre will also bring up your skill level. That's tricky because most people who play jazz standards are very good. You can't start out very good, and they don't appreciate newbies. It's been humbling but I love the genre so I persevere and it has paid off. Not to imply that I'm getting rich off of this
but I am enriched musically.
Starting with Dr Uke gave me a great gateway.
I agree with some of the suggestions below. Find songs that you want to play or accompany. You can almost always find them on the internet. I am probably in the minority regarding ireal pro. I find their arrangements to be unnecessarily complex. Also I don't want to learn 3000 jazz standards. Maybe 100 but starting with 5 is a good beginning goal. Then keep adding songs I want to sing. Start small. Good luck and keep us posted on your progress.