I did this immediately when wordle came out, too. Here's what I got for top 5 starting words along with the entropy:

"tears" 6.00570508021708 "teras" 5.95925128791865 "teals" 5.90122552646963 "tares" 5.88711668336419 "lears" 5.86158270234831

Using another metric which I called consistency (I think it was just minimizing the biggest bucket possible afterwards, trying to beat absurdle fast), the best starting word was tied between "arise", "raise", "aesir", "reais" and "serai". All of these have a worst-case scenario of 168 valid words remaining.

I find it interesting that different implementations seem to come up with slightly different rankings. Maybe the dictionaries are different?

A couple years ago, I wrote some js to sort a 5 letter word file. The value for a word was based on letter frequency in each letter location. Then I took the words that didn't have repeating letters. The I choose a word at the top that I liked and grep'd for some other words to use for the 2nd and 3rd try. In 3 tries, you have used over half the alphabet and all vowels. This usually lets me get the word by the 4th try. Here are some word sets you can start with.

- pares, moity, bundh|bunch - pares, monty, build|guild - pares, doily, bunch|munch

- pores, banty, guild|mucid - pores, canty, build|guild - pores, manty, build|guild

- bares, ponty, guild|mucid - bares, moity, punch|dunch - bares, monty, guild|child

- cares, ponty, build|guild - cares, moity, bundh|gulph - cares, monty, build|guild

I think it depends on whether you use a conventional dictionary as the population of possible words, the valid guess list, or the (known, at the time, for the originally version of the game at least) possible solution list. I guess you could also use the possible solution list minus the words that had already been guessed in previous iterations.

I mean, you had to give yourself an artificial constraint because IIRC the next solution was actually built into the page anyway, not obfuscated in any way.