"Char" was originally simply short for "character", but came to mean a data type for a variable intended to hold character data. I have not seen it used outside of a technical programming / computer science context.
"Text length: x chars" would be perfectly well understood in a technical programming or data processing context. If people other than technically oriented computer specialists of some sort are the audience, then "Text length: x characters" would probably be clearer and better. Even for a technical audience, the longer form will be understood perfectly well, and may actually be clearer if dealing with international unicode characters which require multiple bytes of data. (Note that Unicode can be stored in other forms than UTF.)
When referring to the actual data type in a technical context, "CHAR" should be preferred to "character". In SQL "CHAR" is the name for a datatype storing one or multiple characters, and NCHAR for the datatype storing unicode international characters, for example. Other languages may have slightly different usage.