What is the longest Wordle game?

Question

If you play Wordle in hard mode, with unlimited guesses, then you must solve any puzzle eventually. This is true because there are only a finite number of valid five-letter words, and it is not possible to repeat an incorrect guess in hard mode.

What is the longest possible game of Wordle, if unlimited guesses are allowed, but every guess has to be consistent with the hints from previous guesses?

Here is a valid 19-turn game in hard mode. Is this the longest possible?

1. CILLS
2. DILLS
3. FILLS
4. GILLS
5. HILLS
6. JILLS
7. KILLS
8. LILLS
9. MILLS
10. NILLS
11. PILLS
12. RILLS
13. SILLS
14. TILLS
15. VILLS
16. WILLS
17. YILLS
18. ZILLS
19. BILLS

Answer 1

I think the puzzle description is ill-formed: You say "Here is a valid 19-turn game in hard mode," and then show a game ending in BILLS. But BILLS is not a possible target word! So this is not a valid hard-mode game — no more than a game ending in AALII would be.

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Major edit: My original answer had said, "I think anything allowed by hard-mode Wordle should be allowed by this challenge." But it turns out that NYT's Wordle actually permits all kinds of dumb guesses! For example, if your first guess is "🟨🟨⬜🟨⬜ ROOTS", a human would deduce that (1) the first letter is not R, (2) there is exactly one O, and (3) the target doesn't contain S. But Wordle happily accepts the second guess "🟨🟨🟩⬜⬜ ROTOS" which violates all of those deductions. In fact, Wordle happily accepts six guesses of "🟨🟨⬜🟨⬜ ROOTS" in a row! So, "what Wordle actually accepts" turns out to be an awful guideline for this puzzle.

My new suggested guideline is "Any word you guess must be logically consistent with all previous clues."

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Another question is whether we should then limit the player to guessing only common words, e.g. guessing AALII or BILLS would be disallowed, since those aren't possible targets. But allowing uncommon words is more fun! So guessing AALII or BILLS is perfectly allowable, even though the human player might know those can't possibly be the target; because we're not trying to guess the target; we're just trying to play the longest possible game.

Still, restricting the search to just the common words does prune the dictionary and speed up the search. My best game so far which happens to use all common words (even though I think that shouldn't be strictly required) is length 9.

🟩⬜⬜⬜⬜ SASSY
🟩⬜⬜⬜⬜ SOOTH
🟩⬜⬜🟨⬜ SQUIB
🟩🟨⬜⬜🟩 SIEVE
🟩⬜🟩⬜🟩 SMILE
🟩🟩🟩⬜🟩 SPINE
🟩🟩🟩⬜🟩 SPIRE
🟩🟩🟩⬜🟩 SPICE
🟩🟩🟩🟩🟩 SPIKE

Using uncommon words (but legitimate target word SIGHT), I have length 18:

⬜⬜🟨⬜⬜ JUICY
⬜🟩⬜⬜🟩 ZIZIT
⬜🟩🟩⬜🟩 GIGOT
⬜🟩🟩🟩🟩 AIGHT, BIGHT, DIGHT, EIGHT, FIGHT
⬜🟩🟩🟩🟩 HIGHT, KIGHT, LIGHT, MIGHT, NIGHT
⬜🟩🟩🟩🟩 PIGHT, RIGHT, TIGHT, WIGHT
🟩🟩🟩🟩🟩 SIGHT

Answer 2

Following the logic from Quuxplusone's answer:

• Target word must be a valid Wordle answer
• All words must be valid Wordle guesses (using the list provided by OP)
• All guesses must be logically consistent with all previous clues

I now have a length 19.
RIVER:

⬜⬜🟨🟨⬜ QUERY
🟨⬜🟨🟨⬜ EERIE
🟨⬜⬜🟩🟩 ICIER
⬜🟩⬜🟩🟩 TITER
⬜🟩⬜🟩🟩 PIPER
⬜🟩⬜🟩🟩 NINER
⬜🟩⬜🟩🟩 MIMER
⬜🟩⬜🟩🟩 BIKER
⬜🟩🟩🟩🟩 WIVER
⬜🟩🟩🟩🟩 VIVER
⬜🟩🟩🟩🟩 SIVER
⬜🟩🟩🟩🟩 LIVER
⬜🟩🟩🟩🟩 JIVER
⬜🟩🟩🟩🟩 HIVER
⬜🟩🟩🟩🟩 GIVER
⬜🟩🟩🟩🟩 FIVER
⬜🟩🟩🟩🟩 DIVER
⬜🟩🟩🟩🟩 AIVER
🟩🟩🟩🟩🟩 RIVER

3 unused letters: O, X, Z

369 unique answers (potentially incomplete)

Answer 3

Building on the example in the question, and the comments and answers afterward, I managed to get a list of 22 words:

    AQUAS  _ _ _ _ ■
    LEXES  □ _ _ _ ■
    OLIOS  _ □ □ _ ■
    CILLS  _ ■ ■ ■ ■
    DILLS  _ ■ ■ ■ ■
    FILLS  _ ■ ■ ■ ■
    GILLS  _ ■ ■ ■ ■
    HILLS  _ ■ ■ ■ ■
    JILLS  _ ■ ■ ■ ■
    KILLS  _ ■ ■ ■ ■
    LILLS  _ ■ ■ ■ ■
    MILLS  _ ■ ■ ■ ■
    NILLS  _ ■ ■ ■ ■
    PILLS  _ ■ ■ ■ ■
    RILLS  _ ■ ■ ■ ■
    SILLS  _ ■ ■ ■ ■
    TILLS  _ ■ ■ ■ ■
    VILLS  _ ■ ■ ■ ■
    WILLS  _ ■ ■ ■ ■
    YILLS  _ ■ ■ ■ ■
    ZILLS  _ ■ ■ ■ ■
    BILLS  ■ ■ ■ ■ ■