Formatting date depending on current date
It's neatly formatted and follows standard naming-conventions. I found it easy to follow the logic.

I'm not sure why you switched from a String to a StringBuilder. It doesn't buy you anything, and makes the code more verbose. (If you did it as an optimization, the effort is misplaced. These days, Java compilers turn simple String concatenations into StringBuilder appends behind the scenes. In any case, even if you were doing this trillions of times in a tight loop, the possible savings from StringBuilder would be negligible compared to the time to format dates and whatever I/O you're doing).

Rather than using a static method, you could create an interface (e.g. DateRenderer) and one or more implementations. This would be a bit more object-oriented and more future proof. You wouldn't have to add the alwaysShowTime flag (or whatever future formatting options might be needed) to the interface, but have that knowledge in a specific implementation.

What is the foreign character string when daysDiff == 1? If it's not a typo, it might be worth writing a comment to explain, for people who can't read that language.

I'm not sure that TIME_TEMPLATE_TODAY is the right name, nor whether it is necessary. You don't use a constant for the other date/time formats in the method.