Phew, Movable Type 4 templates
Finally, I moved my templates to be compliant with MT4. I am not sure why it happened, but I needed to recreate all my templates (not styles, but really the underlying structure) that were originally made under MT version 3.1.
The most tedious part was to get the default templates of MT4 to appear, as there were no default templates in my backend, even after running the mt-upgrade script. I didn't read readmes, so don't know if that was to be expected until some official release, but I really wanted to try the built-in styles (such as this one here, Hills Green). To get the default templates, for index templates, I first had to change the template type for existing indexes from "custom index template" to whatever it was supposed to be - and as for those that did not exist, create a blank one, while guessing the names of the templates to be (can be based on previous versions of MT) and then do a "refresh template" from the plugin action drop-down menu (it's a preinstalled plugin).
Also, all the widget that I previously had were not good with the built-in styles CSS, because they used "modules-*" as class/id names instead of "widget-*".
Also, interesting news about Movable Type is that Six Apart announced an open-source version of MT (this site is currently using MT4 Beta 7).