I think it has always depended more upon what is in the actual traffic order, although the previous TSRGD did specifically allow setting down in a bus lane, which the present one doesn’t. However, you cannot enforce against someone stopping to set-down or pick up unless there are “no stopping” or clearway signs, but even then there are the exemptions you refer to in TSRGD. An authority has to provide signs that give “adequate guidance” of the underlying order.
Bus stop clearways (and entrance markings) need a fuller description in TSRGD itself as to what is allowed, as there probably will not be a traffic order to refer to.
I’ll have a more detailed look next week at the difference between the old regs and the new ones in this regard.