I mostly find papers to peruse through Twitter & Reddit, they're mostly on Arxiv. If I'm looking for something specific I use Google + Semantic Scholar.
I would be interested in a tool to help me get a sense for the "research neighborhood" of a paper. Often I end up finding a paper, then looking up the papers it references, and then finding the papers that reference that paper; it's annoying and I'm sure I miss things.
Would I pay for it? Maybe. If it actually helped me find useful papers on the topics I am actually working on (in industry), I would probably pay for it. But the key word is useful; often I search for topics that I think "someone must have worked on this problem before" I find approaches that are great for getting papers published, but not really practical to apply.
What do you think? Is my haphazard approach missing papers that can be readily applied, would having better tools help me find them?
Re reading & collating; I used Zotero for a while. It was ok on one computer, didn't do anything on mobile (which matters since I read a good amount of papers on my phone on the subway), and the need to manually categorize papers sucked, if I wasn't careful I'd get one big "To Read" folder. Having something that automatically organized the papers I'd found for me would be nice.
Would I pay for a better Zotero? Probably not. It felt good to catalog interesting papers, but I didn't really find it super helpful. But I'm not an academic, so I could see this being useful when needing to write citations.