Apologies for the late reply. It's been that long since I've done Connections.

but like it doesn’t tell you to in the “how to play”… It doesn’t tell you to solve it in any particular order at all…

Does it give you any indication you’ve done something special if you get them in reverse difficulty order?

It does, but only if you use the "Connections Bot" option it displays after you've solved it. I think you're supposed to have an account to use it, but I think the "Bypass Paywalls Clean" extension works to let you view it without. Something I've done in my browser is letting me access the Connections Bot without an account, anyway.

Connections Bot gives you a score out of 99, with 99 being for a no-errors reverse rainbow. I got 97 today for 🟪🟨🟩🟦 with no errors.