You can have TOTP as a browser extension. Not saying you should, just that there is a possibility. A bonus is easier backup of secrets so loosing your phone does not lock you out.

You can use a YubiKey for 2FA, I think even for TOTP, but as I am a Smartphone user, I use my phone when only TOTP is available.

I haven't yet encountered situations with mandatory 2FA, but indeed, this is the kind of thing I expect to become widespread, making it more and more difficult to those without a smartphone.

Company TFA is less of a problem than other things as they’ll use a token rather than SMS and you can always use a hardware token. I have a soft token on my phone but it’s not required.

Not really; very few 2FA methods are tied to a specific smartphone app.

You can use TOTP on your PC too.

Yubikey is a good alternative