Slice the 471-line button file into three modules with single
concerns: the popover shell stays in `executor-settings-button.tsx`
(168 lines, just trigger + popover layout + icon/status dot),
`executor-environment-info.tsx` owns the env detail rows + status
badge, and `hooks/domains/session/use-task-environment.ts` owns the
fetch/poll/reset lifecycle alongside other session hooks.