One of the extensions that suspends idle tabs can protect me from this?
It doesn't run stuff when you're the tab is backgrounded (browsers already heavily reduce what sites can do when not in focus[1]). Instead, it just lets you delay work until the page isn't doing anything else (such as rendering the page). For example, you might do this when updating a visualization on a page so that the other updates can complete first (e.g., update the input UI and redraw the visualization when that's done).
[1] https://blog.chromium.org/2020/11/tab-throttling-and-more-pe...
Seriously, web devs need to learn to respect my battery and electricity bill more.
It's not about doing stuff in a tab that isn't in focus. "Idle" refers to the main thread idling in the page you're currently using, so it's about controlling the execution order and priority of JS tasks. E.g. on Google Maps you give priority to rendering the visible map tiles while deferring preloading the surrounding non-visible tiles until the main thread is unblocked (and thus idling).