In the US (assumption that you are in the US based upon how you asked the question), the FCC does not require tower data nor do they catalog that information. So any data on cell phone towers are based upon community wardriving efforts. If there’s nothing there, either you need to collect the data yourself, or hope someone collects it for you. That’s why there’s no conclusive app.
In terms of going from wifi -> cell signal and having a delay on Spotify, I don’t have that issue. An imsi catcher would mimic a tower; that wouldn’t introduce a lag or delay. The handshake would be nearly identical.
If I set up a stingray beside a regular tower, most end users wouldn’t know. A data delay would seem to lead me to believe it might be how you’ve set up your cell phone’s access to data and internet connection.
As in, do you have a network kill switch on for a VPN? Or do you have automations that delay access to cellular data? Is all data going to an app to show you in/outbound connections? It seems like the time delay might be getting an IP from your carrier and whatever configuration you might have that’s exacerbating it. Does this phenomena happen everywhere else when you’re on Spotify/personal wifi -> cell? Again if you’re worried, you need to debug and diagnose it. What that looks will depend on your risk assessment.
If you want to learn the vulnerabilities, learn how cell phones work; the underlying technology.
As for how to learn it? It’s like trying to sprint, when you just learned how to walk. You’re trying to learn very technical information. Read how cell phones work. Then specific mobile network technology. Like how does LTE work? How does 5g work? Etc… until you understand.
Learning is hard. It takes time and effort. No one is going to spoon feed you this information. It took me a hour to learn the basic concept. However it took years of experience to truly understand.
Good luck.