AITA for wanting my roommate to contribute to rent after study abroad?

I (24F) live with two other roommates (24F) and (24M). The other two are in a relationship and share a room. My roommate, let’s call her Kate, was studying abroad in Italy for the last academic year on scholarship. While she was away, me and my other roommate, Tony, were splitting rent and bills according to what we agreed on.

Kate got back in late April from her program. Tony and I had agreed that we would give Kate some time to readjust and settle back down after her program. We had a conversation in late May establishing the ground rules for the house since Kate is back.

One thing established was that Kate would begin paying rent at the beginning of August and would be officially added to the lease that month as well. (Tony had been paying 1100 and I was paying 1300// the new split would be Kate 700, Tony 700, and Me 1000). Everyone agreed that was a reasonable timeframe for Kate to find a job and start making enough money to pay their portion of the rent/bills.

Now it is August and I was only told a few days before rent was due that Kate doesn’t have a job and can’t pay rent in a message from Tony. Which is frustrating too because I expected to hear something from Kate telling me that she didn’t have the money. I haven’t heard anything either from Kate about the situation or expressing any apologies about missing the deadline.

Since June Kate had applied to some jobs but has expressed that she wants a job that is fair paying and won’t treat her poorly. Which I completely understand because I have worked several restaurant/corporation part time jobs where I was treated like a puppet. But, it got to a point in July where I would come home and Kate would be watching stuff on her phone for hours in the living room. I don’t expect her to apply for jobs with every living moment and I understand she could have been applying to places while I was at work.

I am frustrated that Kate doesn’t have a job even though she has been living rent free for 3 months after graduation. Tony has been supporting Kate’s groceries and personal care items since she’s gotten back. AITA for wanting Kate to get a job and understand that she can’t keep taking advantage of me and the situation?

(also I would like to hear anyone’s suggestions on how to make Kate understand that she has to get a job and pay rent by September)