Just because there isn't a standard UTF-8 symbol (yet) doesn't mean ₿ is the correct answer either.

₿ is widely known to refer to Bitcoin, not sats.

You're, at this point in time, more prone to find someone that knows the symbol depicted below to mean sats, than ₿ - That's the current reality, that's how things evolved, for better or worse.

I think it's one of those "pick your battles" situations - Given how entrenched it is at this point, it's worth really asking yourself what has more worth - Fighting against this particular current, or putting energy into things that improve the current UX landscape.

Well-known sats symbol, as used in Snort.social: