At the beginning of your second buy phase, after you had exited the first buy phase by buying Villa, can you spend coffers?
The rules I found on coffers seem to imply since start of this buy phase (for buys disabling spending coffers). Please point me to a clearer version if I misunderstood that.
The rules I found on Villa indicate you don't do any of the effects associated with ending the buy phase. But that doesn't necessarily mean the next time you enter a buy phase isn't a new buy phase.
The open source (single human vs. bots) game with the same rules as Dominion enforces "this turn" there, not "this buy phase. I'm fixing other rule errors and bugs in that for personal use, so I'll likely change that to "this buy phase" anyway. But in case I end up sharing my corrections, I'd like to keep track of which corrections are technically wrong.