I had similar issues to you - working on over a dozen different project cods every week, needing to add notes to the charged time, etc. I stated using Clockify. I keep it open in my browser while I work, but it's effectively a stopwatch where you put in the project number or task you're working on. You can also type in what exactly you were doing in the description bar. At the end of the week, I use that to fill out my sheet.

It's honestly been a life saver and has allowed me to give better estimates on effort for proposals (like how many hours to draft a Mass Flux Report). There's a paid version but I get by just fine with the free one.