I don't have any links to post but my recollection is that, before it opened it was stated - or at least expected (I don't recall in detail) - that bikes would not be permitted in the Elizabeth Line deep core between Paddington and Liverpool St. But when it opened this was not the case, and they are permitted (outside rush hr)
But bear in mind that the Elizabeth Line is not London Underground. It's not a tube line. Other things that are not tubes include Thameslink, the Overground, the DLR ...
So it's quite possible that there may be a rule somewhere that says "no bikes on deep tube London Underground lines". If there is it wouldn't apply to the Elizabeth Line because it's not a London Underground line. It's a different mode.
Or maybe there is no blanket ban on bikes in deep tubes, just a patchwork of individual bans on each of the Central, Northern, Bakerloo, Piccadilly etc... Which would add up to the same thing really.