There’s a few things at play here. First, generally, we define music as organized sounds. This means someone chose the tones, durations, and timbres of the sounds rather than just being random or ambient. As such, by definition, hearing people chatting, typing keyboards, lawnmowers, traffic, or whatever just isn’t music. That said, these things don’t have to be what we’re used to, we can use different scales, unusual timings, and anything that makes a sound as an instrument.
Specifically when it comes to notes, we’re used to having it broken down into certain scales. Without getting too into the theory, the idea is that there are certain ratios of frequencies that have a pleasant sound to the human ear. For instance, two of the most common are 2:1, or a perfect octave, and 3:2, a perfect fifth. The common 12-note is based on an even temperment that mostly maintains that. Particularly in some modern music, you’ll see musicians experimenting with different tunings to get ratios not in or near that tuning, but that’s really something else. Either way, this is sort of what we expect when we’re hearing music, and random noise is unlikely to have any sort of structure in the frequencies of the sounds that mimics these ratios, so we just won’t process it as music.
Also mentioned is harmonics and timbre, which relates to frequencies. Most common musical instruments have become common because they have certain properties like this. A given instrument doesn’t produce just a single frequency, but has a few others that fit those pleasing ratios and add “depth” to the sound. Pure frequencies are essentially non-existent in nature, so most sounds have other frequencies in them, but they don’t fit in those ratios. Though, of course, you can find music where pretty much any sound can be used to create musical tones. In fact, there’s artists who have made their careers out of using every day sounds to create music, tapping pencils, car horns, weed whackers, etc.
But really, it just comes down to the idea that random noise is precisely that, random. It doesn’t carry any information, and our brains are very well tuned at identifying patterns and selecting for signals that have information, even if we don’t necessarily know what it means. That all said, as a muscian myself, it’s not terribly uncommon for me to find brief moments where some sounds will line up into a brief rhythm or melody or whatever, but that’s not really any different that looking at snow on a TV and picking out an image; sometimes even in randomness, we’ll see a pattern that isn’t really there.