Why is this a check for CO with 100% of range?

I think it's because we play a lot more defensively OOP when both players can have the nuts and other very strong hands. Playing OOP always realises less equity than IP as we're at at an informational disadvantage.
If it was CO vs BB we would do a lot more cbetting as we have a huge range advantage on a board like that and we're IP vs BB. But when it's the BTN that calls a CO open, BTNs range should have a ton of broadways so we really don't have much of a range or nut advantage.
If you think your opponent doesn't have as many broadways in their range as solver does and is mostly calling just with pocket pairs preflop it would change the strategy a lot though and CO would be able to start cbetting more

CO is opening very wide and BTN calls a tight range (or is supposed to in solverland). They have a much higher concentration of KQ, AJ, AT, TT, etc...

The primary strategy for the Cutoff (CO) on this A♣ J♥ T♠ flop is a near-total range check (95%). This approach dictates checking almost every hand in the range, including premium holdings such as straights with K♠ Q♠, trips with A♥ A♣, and two pair with A♠ J♠. Even a strong Top Pair Top Kicker holding like A♥ K♥ is played as a check the vast majority of the time. This “range-check” strategy is a standard GTO response when the player out of position (OOP) faces a board texture that connects extremely well with the caller’s range.

The logic behind this passivity is rooted in the positional disadvantage and the high connectivity of the board. Although the CO holds an equity advantage of approximately 55.8%, the A♣ J♥ T♠ texture is exceptionally favorable for the Button’s (BTN) calling range, which is dense with Broadway cards and potential straights. By checking the entire range, the CO protects their weaker “air” hands and prevents the BTN from playing perfectly against a split range. Keeping the checking range “uncapped” with hands like A♥ K♥ ensures that the CO can profitably defend against the BTN’s aggression and realize their equity across various turn and river runouts.

Range advantage of opponent makes it 100% check

man, I don't know if you realize how bad ChatGPT is at poker. Can't even calculate the hand strength if you provide 7 cards.

but I guess this means my reply reached some quality standards

Snap call.