I can give you exact dates, I just didn't bother to look it up. You can see it in this address [1] which is a Celsius-owned payment rail between tether treasury and Celsius trading addresses.
The exact transactions start here [2] (aug 11, 2021). I got the date wrong in my previous post because I didn't remember and was too lazy to check.
As for your misreading of legal documents and misunderstanding of how loans are written:
The loan was not written in May 2022 -- it was written prior to October 2021, when its existence was confirmed. The loan is denominated in BTC at the price at which it was underwritten (early August 2021, BTC price low-mid $40k)
The fact that BTC dropped 30% in may-june 2022 has no relation to the total loan value from Celsius' side. It only changes the amount of collateral tether would be margin calling Celsius for.
Celsius faced a margin call in May 2022 (price 30k) because the loan was written around a BTC value around 30% higher than that (~40k). Note the math checks out here as well.
It took over a month for the margin call to result in liquidation, hence tether's loss of $250-300m at a price of $21k. If tether immediately liquidated in May 2022, they would have skated by without a loss.
[1] https://etherscan.io/tokentxns?a=0xd41cdb2a35a666e8e1f9f5305...
[2] https://etherscan.io/tx/0x367f433872789fa0223d6ca93c6e073a72...