Do you know what’s the technical term to search if a phone has that capability? Asking for an iPhone

Unfortunately, iPhone can't bridge wifi networks, which makes travel routers particularly useful if you have an iphone, and a laptop, and are staying at a hotel with wifi.

Like WiFi tethering?

My iPhone calls it personal hotspot.

It's my understanding that personal hotspot can only utilize the cellular connection for the internet side since the wifi connection is being used to connect clientside. If one is hoping to use hotel wifi rather than their cellular plan data, Apple's solution won't work.

I'd be happy to be proven wrong on this however.

Not only new and expensive, my 5 year old budget phone could do it (a vivo).

Budget Chinese phones often have features that only expensive American or Korean phones have.