Is it wrong to wait until application approval to disclose having an ESA? (Emotional support animal)

In regards to fair housing laws, when do I need to disclose to a potential future landlord that I have an emotional support dog? Is it wrong to wait until my application is approved? Rentals currently are moving quickly, especially the nicer ones and I’m under a strict budget. A few places I’ve mentioned it to have been completely fine w it, saying it’s not relevant as they can’t deny ESAs, and they simply need a letter prior to moving in. Others (typically the ones in nicer areas) have either ghosted me after “needing to check” or have delayed in getting back to me, then rented out to someone else.

I used to work in hiring at my old job, and I know it’s still very easy in the application process to get around discrimination laws. Just wait until another candidate comes along and fill the position, ghost them, or tell them you’re taking it in another direction. So I’m pretty sure the same could be happening with the apartment search.

I’ve had my dog since she was 8 weeks, and trained her since 10 weeks. She’s also about to test to be a certified therapy dog (she was supposed to test in April, but centers got closed down due to Covid and have yet to reopen). She’s now a year and a half and very well trained (which is not necessary for ESAs at all, so I understand why landlords could be nervous).

However, legally they do have to allow support animals due to the fair housing laws. Everything I can find says you need to disclose to your landlord, but I’m not sure of the process as to when I need to tell them, especially when I suspect some places are turning me down bc of it (my credit is really good, I have a good reliable income, and credible references from past landlords).

Is it wrong to wait until the application is accepted and the actual move in process starts to disclose, or when do I need to tell them?