Former employer submitted separation certificate to Centrelink saying I chose to leave, even though I wasn't offered any more shifts, but is saying to me that they have no idea about submitting anything, and I am still in their rostering system

Bit of a weird one,

I worked a second casual job last year for a few months, then went on holiday in early december. I booked the time off appropriately but once returning from holiday I never received any further shifts in the roster. I wasn't worried about this as I have another job and just assumed that they were silent sacking me.

My old work mate messaged me yesterday asking if I would like to get some more shifts as they need the staff (former employer would always tell this mate to message me if they needed anything, they didn't want to message me themself sometimes, I even found out I got the job through this mate), but I thought I got the sack?

Now that I am enrolled in study next semester, I have submitted a claim for youth allowance, and once I got to the employment history section of the claim, it showed that the employer reported that I chose to quit, which is most definitely not the case.

I messaged the former employer (owner operator of the store) today asking for them to amend it as terminated and not resigned as I don't want it to affect my claim at all, but they stated that I was never terminated, I'm still employed, and that because I didn't message them after my holiday, I wasn't getting any shifts (end of my holiday was clear on my leave calendar btw)

After some back and forth I asked them to clarify whether I have been terminated or not, to which they replied "No you are not terminated yet". After this reply I sent the screenshot of the previous employer part of my youth allowance claim, showing the employment separation details as "employer reported", the date ceased work for employer as a date that I was currently on holiday at that time, and the reason ceased work for employer as "chose to leave". I say this implies that they submitted a separation certificate.

They then says that it isn't possible, I'm still in the rostering system, it isn't from their side at all, and they have no idea.

They then ask me if I still want to work for them, to which I haven't replied

What do I do?