I've been meaning to build something similar for some time and never got the chance to do it. What you built looks really good and does almost everything I had planned.
The main feature missing for me (the one I wanted to build first if I ever started) is a dashboard with all (start/pause) buttons with current tasks ready to be clicked. Let's say I'm working on ticket TICK-123 and also "customer care". Then I would love to have a dashboard with a start/pause button for TICK-123, "customer care" and a "new task" one that behaves like the "Start stopwatch" you have. That way start/pause is one click away and tracking time is less in the way of what I'm currently doing.