Will the new owner still recognize the day off I already booked before the sale?

In most cases, yes, and there's no good reason a new owner should treat a previously approved day off differently just because ownership changed hands on paper. Your continuous employment carries forward the underlying rules that already governed your time off, and a day already properly approved under your existing employer's process is generally a commitment the business should honour, since you made your own plans in reliance on that approval.

Where this occasionally gets bumpy in practice is a records or communication gap during the transition — if the approval was only tracked informally, or the new owner's scheduling system doesn't have your existing approval loaded in, it can look to a new manager like the day was never actually approved, even though it was. That's usually an administrative problem, not a legal reset of your existing arrangement.

If you have anything in writing, an email, a scheduling confirmation, a text from your manager, hold onto it and share it proactively with the new owner well before the date, rather than waiting to find out at the last minute whether it carried over properly. If a new manager tries to walk back an already-approved day off with no real reason, push back on that directly.