Earlier quoted context omitted.
Well, except for the cases when you happen to have the entire VM for your language running in the same tab where you program lives, and they both are all JS. Probably harder, and wouldn't work equally well for everyone, but it would be possible to have "guess language and autocomplete" entirely client-side, especially when it comes to JavaScript of all languages.
It seems like the main disadvantage would be that you have to load all the autocomplete data / model weights on the client-side and your webpage might be CPU/memory limited
Not sure what "model weights" you're talking about, but yes, that is the trade-off. Although complete autocomplete data for the entirely of the JavaScript APIs would be what, in an efficient format, easily below 1MB at least.