It seems to be hit or miss for some people. Some get it to work, others don't. Maybe it only works on Pixel 6 / Pixel 7 or their pro versions? Check if it works with Airplane mode on. If it works, the language packs were downloaded.
I did some digging in to this a while back and found that the offline speech pack was 25 mb at the time (October). Not sure if it's the same size now, but I'd imagine it's a similar size. My phone downloaded the file in 9 seconds. There's no loading bar or anything. GBoard just starts downloading immediately after you switch the feature on.
I don't know which variants of English they support now, but the following were supported when I checked last: Australian English, Canadian English, British English, and American English. Maybe verify you have one of those Englishes selected under the languages option. If you speak a language other than English, I'm not sure which languages are supported.