I was able to go from 5 to over 20 parallel sessions without burnout by changing my role. I switched from engineer to engineering director. I try to focus on directing and deciding. I built a software for that for myself. Two key features:
1. Each project (= one or more repos) gets a canvas. On it, work is laid out as cards. Position and color let me build a mental map.
2. Agents end each card with a demo, which is typically a narrated video of the new feature or bugfix. I review it like an engineering director in a launch review. If I have comments, the agent goes another round.
With this, I don't feel the pain of context switching because I don't need to keep the context all in my head in parallel. I get it presented every time a card wants something from me.
I totally get the task board and I do almost the same thing myself. The demo idea is cool though. It makes sense that whenever the coding agent wants some judgement from you it spends a bit more tokens to make a report optimized for a complete and readable explanation. I doubt it should be a video (videos impose a minimum time required to get through them), but there's certainly a lot more you can do compared to coding agents' default text responses.
I find the time unproblematic. A bug fix is typically 30 seconds, a new feature 1-3 minutes. I want to review those before they go out, and any other way to review them I can think of would take longer.
FWIW, if the work is better shown on an HTML page (e.g. to show stats of a previously flaky test), the agent can do so.