Google sheets have worked well for my team in the past. We listed each individual finding in a single row, making sure it describes a single item. Then in the following columns you'd include more details such as possible trade-offs, reasons that might have caused the issue, even ideas for improvements (as they often come during while you're testing). You can also include columns that capture number of times a particular issue occurred, its severity, priority etc. As the number of studies grow you can start adding new sheets to the document, and later start creating new documents and folders.
I'd be against using a separate software just for capturing UX findings. Your development team will be reluctant to use it. And if they do they will gradually stop visiting it over time. You probably already use Google Docs for other things so there should be less friction.
In terms of integrating this into agile processes. I think it'd be good to schedule for occasional UX Review sessions (similar to Design spikes) to go through the most recent studies, discuss the issues, assess collaboratively their severity, uncertainty, and possible dev / design costs. Based on this information the product team should formulate stories that get integrated into the following sprints.
One extra note. Many usability experts recommend inviting people from outside the UX team to usability studies, just to observe. Especially people that are later involved in working on solutions to the identified problems (e.g., devs).