Lots of hardware supports being operated in access point mode and station mode at the same time -- on the same radio/antenna(s).
Even the venerable (and ancient) WRT54G could do this with appropriate firmware.
IIRC, I've even used this functionality with Windows ICS on my laptop many moons ago
It's not necessarily an efficient function, but efficiency isn't always the most important thing.
(These days, I often travel with a Mikrotik device that I've set up to be a hotspot abuser, so as to provide myself and whoever is with me a slice of Internet while having the immediate appearance of being a solitary device. It does this trick very well indeed.)
Even the venerable (and ancient) WRT54G could do this with appropriate firmware.
IIRC, I've even used this functionality with Windows ICS on my laptop many moons ago
It's not necessarily an efficient function, but efficiency isn't always the most important thing.
(These days, I often travel with a Mikrotik device that I've set up to be a hotspot abuser, so as to provide myself and whoever is with me a slice of Internet while having the immediate appearance of being a solitary device. It does this trick very well indeed.)