I don't believe it's related to fth files, as they manage the layout of the customizable area, not the basic menus which are also missing. A complete uninstall, meaning both install folder and all those AppData litter folders.
They do but not entirely, the menu should still be there saved for other customization to the toolbar, this bring me to the revelation that the OP is using Columns UI. @OP: Was your previous config using this or DUI?
I feel that it's a much better policy when doing a stardard install to keep all configuration files, etc, in the install folder. Don't mind that thing of not being able to update components from within foobar. Many components don't even work like that as they're not on the official components page, and it makes a world of difference when it comes to making periodic foobar install backups.
It's not recommended to save user specific settings in program installation folder, it's Windows doctrine that should have been done before but not until Vista that it has been promoted, Windows is a multi user system for what it's worth. Install as portable and you'll have your mentioned behavior.