Relocate the light/dark toggle button out of #app1 and into a new
#app3 mount just before the back-to-top element so keyboard focus
reaches it near the end of the page instead of right after the main
nav. Replace the library logo's reactive :src binding with a plain
src plus data-light-src/data-dark-src so app1 no longer needs any
theme state; app3 now owns toggleTheme, overlay updates, logo swap,
and the OS preference listener.