How much privacy does Lightning actually have?
Bob only knows the channel R3--Bob and his other channels.
in particular due to the onion routing Bob has no way of knowing who send the payment or say anything about the channels of the sender (as Bob does not know the sender)
Routing only know their incoming and outgoing channel. So the only thing that R2 would know is that there was and HTLC offered by R1 and that it is supposed to be forwarded to R3.
With respect to your question of how does Bob know about Alices channel. As said Bob doesn't but you could invert the question. If alice wants to pay Bob, how does she know about the R3 - Bob channel? There are two possibilities. Either Bob specified a Routing hint in the invoice or she does so (with other channels on the path) with a probing trial and error approach. This is well described in https://arxiv.org/abs/2103.08576 where this was also used to probe for the balance values of channels. In that sense the information on Lightning Network is not strictly private.
However probing takes time and might be inacurate as there are counter measures to probing channel balances. (In comparison if you see something on chain it is pretty clear that this is the reality)