I think investing in a little lighting and getting creative with lighting goes a long way. I don't think shooting manual will improve your shots that dramatically. If I couldn't shoot fully manual RAW files straight out of my phone I would probably shoot with Lightroom like @Natchraz mentioned, it's also worth it to spend some time with edits.
I had mentioned lighting, maybe consider investing in a NEEWER CN-160 and a cheap Amazon tripod. You can get both on Amazon for a total of $37 and if you decide to get a camera later on you can still use them. There's a ton of cheap colorful scene lighting you can invest in. You can even use flashlights and glowsticks to help light your scene. Finally I wouldn't be afraid to use built in flash especially with the right edits. It looks terrible if your subject is a person or if you're shooting an entire scene but for right documentary style shots it's not the worst thing.
Finally, I would try to focus on other aspects of photography that aren't limited by the camera you use. Try to work on the composition of each photo.
Some links:
https://www.amazon...pa_i_a8hMEbY0D8MVE https://www.amazon...pa_i_J9hMEb79VZCZ5 https://www.amazon...pa_i_z-hMEb12YVTZ6