No — Berkeley Mono isn’t listed as a free font. The link at the top of this page goes to the source, where you can check licence options.
Berkeley Mono™ is a love letter to the golden era of computing. The era that gave rise to a generation of people who celebrated automation and reveled in the joy of computing, when transistors replaced cogs, and machine-readable typefaces were developed, for when humans and machines truly interfaced on an unprecedented scale.
A1 features 6 websites using Berkeley Mono, including Interfaces, Linear, and Detail. They lean towards Animated, Minimal, and Dark design styles, and they’re most often built with Next.js and Framer.