An extension throws "Class does not exist" after the upgrade. Why?

Because the upgrade removed or relocated an API the extension still calls. Magento deprecates classes and methods across 2.4 minors and eventually removes them; a module written for 2.4.4 may call something dropped by 2.4.9, producing Class … does not exist or a deprecation fatal at compile or runtime. We map the old call to its supported replacement, patch the extension (or bridge it), and verify the rendered output, so the module works on the new version instead of being disabled.