Most likely judging by the amount of suitcases visible on almost every train
My experience of Heathrow Express in recent months is not expected to be representative, but I recently travelled both ways and what I saw suggested the Express is still popular.
I was at the very front of the 1625 Paddington to Heathrow on 12th January, so while it was quiet up that end one would expect it to be on a January Thursday afternoon. I travelled back around 0912 on Sunday 15th January, and again while it wasn't packed in my bit of the train there were still healthy loads on. For that time of day on a Sunday, in January, I'd not expect it to be packed. In the peak holiday season, then that would be different.
It is worth mentioning that the 345 in the other platform appeared very busy, but I expected that to be the case. I was a little smug as I left on my much emptier 387!
On other times when I've been at Paddington, the Express does load quite well from what I've seen. Not crush loaded, by any means, but certainly busy.
As for the Elizabeth line, I've yet to have any issues with it. Punctual in my experience, bar once with a signalling issue on a 345 at Stratford, and no issues whatsoever. Some trains I have done have been busy, but by no means crush loaded or anything. Every 5 minutes (or so!) through the core is just brilliant, with huge stations and their platforms, good quality trains, no complaints from me at all!