[Fun fact] Nuntii Latini
Do you know that there was actually a radio station that transmitted news in Latin? They started in 1989 as a sort of joke and they actually stopped to broadcast just this year! Here is the official link of their page (in Latin, of course) : https://areena.yle.fi/1-1931339 It was weekly ~5min world news with transcription. If you want to know the story behind it: https://en.wikipedia.org/wiki/Nuntii_Latini
Their pronounce is delightful to listen to, it can be a very good tool to use it parallel to your studies, it's a pity that they stopped, hopefully someday we can have something similar back.
When they stopped they were thinking of putting out a podcast, which would be great. So far there's no word of it that I've heard, however. Although their accent wasn't quite 100% "restored," it was perfectly understandable and was great listening practice. The broadcasts were marvelous and, you're right, really worthwhile. . . . Where else could you hear much news about moose, especially in Latin? Except maybe here.
His Latin is very good. Well pronounced and quite fluent. Really good for listening practice, and he has plenty to say that's interesting. You should give his websites a try. Lately there has been quite a bit of audio/video posted online that provides great practice. If you would like a listing of good online sites, this is pretty good; links are given in the "SHOW MORE" info, below. . . . Latinitium has good links, too.
Radio Vatican also has a weekly news podcast in Latin — Hebdomada Papae — that only started this year. You can listen to it here: https://www.vaticannews.va/it/podcast/rvi-programmi/hebdomada-papae.html
Though, as far as I (as a Latin newb) can tell, they don't use classical pronunciation, but ecclesiastical.