I know the question is rather awkward at first and I am possibly overlooking something, but I would like to know something I really don't understand.
In the past I have used modified versions of Spotify and they are fine but obviously no modified version allows you to download songs because it is a premium function at server level and honestly I would like to have my songs on my device, so if I don't have internet I can still listen to them.
After those modified versions of Spotify, I have used apps like ViMusic, Spotube and SimpMusic which are basically Youtube Music apps but without ads and with more features, including downloading music, the problem is that they do that at the level of the app itself, not in a separate file. And I love these apps and I can not recommend them enough but my phone is a little old and I see 0 need to change it since I use it for basics usage and although this can sound dumb the interface of these apps are full of blur and unnecessary effects that make my device slow, including Spotify, and I don't like Spotify Lite because I feel it is a very trimmed version of Spotify.
So this is where my question comes in, for those who exclusively download music, how do you discover new songs? Spotify's recommendation system is great and Youtube's radio mode is very good but obviously I need to use Spotify or Youtube Music to use it and I prefer to use light apps for local playback because of what I already mentioned.
Edit: Thanks for all the recommendations! I never thought this post would get so many answers and there are too many comments to answer one by one, but I admit that the old-school method of reading blogs or magazines works well, and I also like the idea of sites like Last.fm or discogs.
It's not really like radio, it's a bunch of people running their own shows at times of their choosing. But if you follow a bunch of people who are doing 2-3 shows a week, pretty soon you will find that when you look at the "Following" page to see what's happening right now, something worth listening to is probably on.
Here's what my Following page looks like at the moment: https://i.imgur.com/7OXkRbN.jpeg
Not too good, but it's early still. Only one person I follow is live and it looks like they are chatting instead of playing music, which is unusual (and I won't bother to listen).
There are some recommendations below. If I click Show More, I can see 8 other live streams. (I can see more under the Browse feature.) : https://i.imgur.com/U5Bvec5.jpeg
Some of these 8 I recognize as being not my taste, some show genres I don't care about, but there are a few that I will check out. OK... the reggae dude was playing hip-hop which isn't my bag but I might check back later because I like reggae and ragga. The funk dude was playing great music but wouldn't shut up. SlugRadio is playing some good EBM that is new to me, the DJ puts up a track ID in the chat stream, and most importantly doesn't seem to be on mic all the time. So that's a good find and if the music stays good, I'll probably Follow that channel. (this is what the stream looks like: https://i.imgur.com/cCFPpG7.jpeg)
One other thing...
Twitch lets you watch replays of shows which gives you even more ways to find something to listen to... But, they process saved videos and knock out copyrighted audio, so most recorded DJ streams are mangled. For some reason, Twitch gets away with letting people do anything they want when the show is live, while YT uses realtime detection to mute your stream and issue a copyright strike.