Two papers appear out of thin air.
Recovered Paper II
The Hanged Dog
You can guess one letter or several letters at a time.
Enter one or more letters each turn and see whether your guess keeps the dog happy.
Hint 1
This doesn't seem like a normal hangman (Hanged Dog) puzzle. No matter what you enter (a single letter, multiple letters), you will always get it wrong.
Hint 2
It seems like you need to put in the correct answer all at once to win, but you're not getting that information from this particular paper/puzzle.
Hint 3
Solve the Pentordle puzzle to get the answer to The Hanged Dog.
Recovered Paper III
Pentordle
One five-letter guess will be checked against every puzzle at once. You have 10 total guesses.
Hint 1
This seems like solving 5 Worlde puzzles simultaneously. You get 10 tries before having to restart, but at least you can reset the puzzle!
Hint 2 (Pentordle Solution)
The Pentordle answers (left to right) are: PHONE BOOTH TREAT SAVES POOCH. Maybe you should be looking around for a phonebooth that will give you another hint/answer?
Hint 3 (Meta-puzzle partial solution)
Look around the cafe for anything featuring a phonebooth and some kind of treat.
Hint 4 (Meta-puzzle solution)
There is a poster of a red, British phonebooth, which is the signature tin for "SHORTBREAD" cookies. The answer to the Hanged Dog puzzle, then, is "SHORTBREAD".