This game obviously has the same open world but it's not introduced in quite such a spectacular way (probably because they know most people have already played it).
You could, but I’d definitely suggest playing Breath of the Wild first if possible. TotK is a sequel, so characters already know you, part of the fun is seeing how the map changed, etc.
Also, they’ve added quite a few conveniences that would make it hard to play in the reverse order.
And....no. BotW is still arguably the best game ever. Missing it might not be a great idea. Tough choice :)
It’s actually excellent and if you have a kid it’s great to play with them on a rainy day.
I handle the monsters and Yiga, and heckle during the puzzles.
Playing TOTK it's a drastic improvement over BotW.