No for 4G/5G the line gets a bit blurry there unfortunately.

The operating system vendor can be bribed. AT&T for example asked Apple to show a 5GE icon when an “advanced” LTE network is in use.

That must be a US specific thing. Most phones here in europe aren't bound to a specific provider.

As a matter of fact, the only phone I ever got with a mobile plan was my first mobile phone, a Motorola RAZR flip phone more than 2 decades ago.