There is another situation where you can determine if the word has two of the same letter. If you guess the letter in a different spot and it is correct, it will also turn green. Example..
Let's assume the puzzle answer is CHEEK
First guess is FRESH - "E" in the third position turns green and the "H" turns yellow
The second guess is LOVER - "E" in the fourth position turns green.
You now know the word has two "E's" in the 3rd and 4th positions and an "H" in position 1 or 2.
What about "phone" (short for telephone) or "auto" (short for automobile) or "flu" (short for influenza) - do you consider these abbreviations instead of words? English is an evolving language with new words added regularly. Often, yesterday's abbreviation becomes today's word. All word games need some sort of definitive reference for what is considered a valid word - seems like the Dordle folks are using Wiktionary as their source. If it's in Wiktionary, then it's a valid word.
The game tells you if the letter combo is considered valid - I've learned a couple new words that way :)
So what do you do if you hit 5 letters across the two games? You wouldn't be allowed to add any new letters :)
For example Word 1 is PILOT Word2 is PLANK First guess is PATIO -
First Game returns P (in the right place) and T I O (in the wrong place)
Second Game returns P(in the right place) and A (in the wrong place) By the rule you have suggested. you must use all 5 letters in your guess so you cannot add any new letters :(
