Quoting Michael Paoli (michael.paoli@berkeley.edu):
Yeah, sounds like one of the not-so-timely ones. If they gave the near instant capability, I'd expect they'd have sent you an email, that would also include a link (or other means) to basically say "do this now" - which would make things happen quite quickly.
There appeared to be one last step I was unaware of / had forgotten about: When I checked the IWantMyName customer WebUI this morning for the two domains, each had a green button for me to "approve" the pending transfer. I pushed it. A short while later, the two domains were de-listed from IWantMyName. They status in Gandi has, at this writing, not yet updated, with the detailed step (in Advanced View) showing "Validation of the transfer by the former provider We are waiting for your current provider to accept or refuse this transfer. It should arrive in your account before Jun 8, 2024 unless they refuse it."
WHOIS shows now as a Gandi domains, with the correct nameservers, but the detailed information for Registrant, etc., isn't yet there.
Given that they didn't email with, e.g. link or some other option to make this happen "now" (quite quickly), I'm guessing 72 hours, or whatever that wait period is that allows registrant to object.
To be clear, yes, no e-mail arrived saying I needed to push those green buttons, yet, in fairness, the buttons were presumably there about the time I went to sleep, thus could have OKed the transfer then.