Typically very little. Most current CPUs integrate some variation of the Advanced Encryption Standard instruction set (AES, AES-NI, etc), so just like H.264 or H.265 decoding, it can be very, very efficient with custom instructions (magnitudes of order faster / less power consuming than without).
This is why most devices are equally capable of rendering http or https (you never have to 'revert' to http because a website is too slow in https... it's just not a thing). A stupid background app may consume 10x or 100x your encryption budget.
On a modern CPU with encryption instructions in the ISA, a vanishingly small amount of power compare to the databases and JavaScript involved in the requests.
The somewhat surprising main problem is not CPU load but the additional back-and-forth TLS requires to establish the handshakes. One of the main goals/draws of HTTPS/3 is eliminating these extra steps.
Efficiency is overrated. Encryption stops injection or modification of data in flight in its tracks, that alone makes it worth it. Otherwise, how would you know you receive what the sender sent you?