Smartphone is required for everything there, yes. Signing up for services, authenticating yourself (e.g. when entering a train station), payment, social media, etc.

Computers used to be expensive and people had less money back then, so most of the country essentially just directly upgraded to smartphones. Many don't and never used to own a PC outside of work.

For just SMS authentication, you just need a phone. Any kind of phone.

But it also just so happens that in both of those countries, you must have your identity attached to any SIM you purchase. So, anything that makes you register with your phone number will indirectly link your real identity to that registration. It must be very convenient for their governments!

No, any kind of phone that can receive codes over SMS will work (like the ultra-cheap feature phones you can probably get at your local corner store). From a computer browser, you still enter your mobile number to login, then enter the verification code it sends you over SMS. I've also seen sites that offer phone call as an alternative to SMS, so you can presumably also login from a landline.