Does having the theme pet bar full mean that a theme pet should be guaranteed next play? Cuz the bar is full for me and I played the game and no theme pet. Am I just super unlucky?

It means that the number of theme spots is at its maximum amount (at least 6 spots), so you have the highest chance of getting a theme. It will remain full until you get a play where you do get a theme.
The cards are generated as actual cards with all the potential prizes just hidden, rather than just rng selecting what is appearing when you scratch a spot