The transaction fees page says that transaction cost = lamports_per_signature * number_of_signatures.
Here, is the number of signatures calculated based only on the top-level instruction or are the signatures of invoke_signed() calls also being considered?
No. During invoke_signed(), the runtime artificially promotes the PDA(s) to signers for the duration of that instruction invocation only. Transaction fees are charged up front, before transaction execution and hence we know neither whether, which nor how many CPI calls will be made. Luckily this doesn't matter since, due to the fact that these are runtime driven, artificial "signers", there isn't actually a digital signature to verify, which is what the fee is ostensibly charging for. Instead the CPI invocations are taken from the compute budget.
