It looks like it's a clever double-bacronym, since BAR is also "Balanced Annihilation Reloaded" which is what this project started as. Balanced Annihilation being the most influential and TA-like of the several games built on top of the Spring ( https://springrts.com/ ) engine... which was originally made for TAlikes though there are several other projects on the engine now. Zero-K is also a popular Balanced Annihilation-derived Spring engine game, but is less TA-like.

I think the original Balanced Annihilation had the feature/problem that it used a bunch of a original Cavedog models and Reloaded is carefully avoiding that in addition to visual and gameplay improvements.

I played a ton of Balanced Annihilation like a decade ago and it was already a "better TA" than TA or SupCom in many ways.