Switching to dark theme flashes white on load. How do people avoid it?
Set the theme before first paint with a tiny inline script in the head that reads the stored preference and puts an attribute on the root element. Anything loaded as an external file arrives too late, which is exactly what the flash is showing you.
At what point does a static site need a backend?
When you need to keep a secret or write shared state. Everything else, including search over your own content, can be done in the browser with a prebuilt index, and it stays working long after any server you would have written stops being maintained.
Web font swaps cause a visible reflow. Fix?
font-display: swap plus a fallback stack with matched metrics. The modern lever is size-adjust and ascent-override on the fallback @font-face, which lets the substitute occupy the same space, so the swap becomes invisible rather than merely fast.
Is there a simpler version that gets most of the benefit?
Yes: do the first step, skip the automation, and revisit in a month. Most of the value is in the first step, and most of the cost is in making it repeatable before you know it is right.