I cannot speak to what Windows does during Uninstall. However I am aware each Application has it's own specific Uninstall. Windows is complex enough on its own. Third party product like Intuit's Lacerte potentially causes still more dominoes to fall. At times a riddle, wrapped in a mystery, inside an enigma.

When replacing PC what method did you use? Transfer data from old machine to new via cable or cloud, or backup old machine and restore that backup onto new machine? Likely as you suspect, something went sideways during that process.