There's (2) parts to your question, so I'll answer each in turn:
How does an Access Point Work?
Since I actually wrote "pi-ap"- a Github repo which automates the configuration of a Pi into a WiFi Access Point- I'm in a good position to detail the inner workings of an AP.
In a nutshell:
An AP- in this case your Pi- has a radio in it through which it advertises an SSID for the wireless network.
The AP and clients (which themselves also have radios) communicate using an 802.11 protocol which is set by the AP.
After a wireless client successfully authenticates, it's assigned an IP by the AP.
The number of clients that can connect to the AP is limited by the size of the DHCP pool. So if the subnet is a /28 mask, a max of 14 clients can connect to the AP before the address pool is exhausted and no further IPs are available to assign to clients.
The AP routes traffic for the subnet of the wireless clients to another router which is either directly or indirectly connected to the Internet. Indeed, if you look at your network connection properties in your laptop (or "desktop"- do such things exist anymore?!?!?), you'll see the IP of that AP as your gateway.
Access Point Power Consumption:
Whether the AP has zero clients or a gazillion, the AP's radio is on and using power to advertise that SSID.
Indeed, when conserving power matters, many mobile phone users- myself included- kill their WiFi & Bluetooth on their phones to stop radios from burning battery.
But as an AP is NOT going to be powered by battery, but by a mains power supply, no point really in worrying about power consumption.
I actually opensourced "pi-ap" so folks could get some practical experience with networking. If you're really keen to see how the gears turn inside an AP, I encourage you to download "pi-ap" and use it to transform your Pi 3B+ or Pi 4 into an AP. The scripts themselves are all very well commented enabling you to understand what they do: