[Landlord - Oregon] Tenant not paying pet security deposit

Fresh landlord here.

I have a tenant who paid their security deposit, but not their pet deposit. handed the keys over and said they'd pay the pet deposit later (first huge mistake, i know). Well, they didn't pay and then was late on their Dec rent, only paying a part of it.

I sent them a notice for nonpayment of rent that broke it down like this:

Total Due: $2700
-rent ($2900 Dec rent - 650 partial payment): $2250
- late fee: $50
-pet deposit: $400

They'd have 10 days to pay or the eviction process starts. They reply back saying they'll send the rest of the "rent" this week, but do not say when they'll pay the deposit because that wouldn't "trigger a 10 day notice".

To me, it sounds like they have no intention of paying the pet deposit.

My questions are:
is it true that not paying the deposit wouldn't trigger a nonpayment notice?
Did I make a mistake by implying that the partial payment that they sent only goes towards rent?
Can I send them a new "notice of nonpayment" that reflects the pet deposit actually being "paid" but the rent technically hasn't been paid?

Any thoughts on this is much appreciated! Again, very new landlord so I know this is my mistake...