I have had a similar experience. I would find my sleep schedule constantly drifting later and later, which made it harder to wake up in the morning, so I would self medicate with caffeine which made me anxious, which contributed to the same cycle. But even when I stopped taking caffeine I always found it difficult to actually go to bed at the same time every day.

What finally worked for me were red light glasses. I wear the True Dark Twilights Classics (though I’m sure there are other brands on the market) for 2-3 hours before bed time and I’m actually sleepy. Way more effective than taking melatonin tablets ever was in my experience. And I haven’t even had to substantially change my screen usage either (though the glasses do make everything come out monochrome, which makes it difficult to use anything that’s not in color blind mode).