I’d like to write more but I don’t tend to like my writing for longer than ten minutes after I’ve written it. I’ve gone through the process of putting in my 10k hours in music and gone through the motions of attempting to build a professional music career, so I generally understand that the sucking phase lasts a long time. I also know a lot of it is jumping into the routine of writing every day. Just curious to see what people have to say.
It's normal to not like what you've written after you've done it.
Generally, good writers read a lot, so if you have read a lot of literature, you've likely internalized a lot of it, and that will give you a pretty good foundation alone. It will also make you judge yourself harder.
The typical advice, like you said, is to write frequently. Start small. Set a word limit or something for your writing. There are plenty of writing prompts online. After some time passes, you'll start to see patterns emerge in your writing. That's your voice. You can either decide you like it and lean in or decide that you want to go in a different direction. After some time passes, you'll still dislike most of what you write, but you'll start to notice some pieces that you do like.
That's the general advice, but my personal advice is to focus on things that interest you. Write the things that you want to read. As a musician and a writer myself, I can tell you that you really don't want writing to feel like drilling the fundamentals in music. To me, it's better to go for the things you like and want to do instead of drilling a bunch of shit you don't care about in hopes of being "good" one day.