Switching employers while awaiting ILR decision?

I’m on the occupational shortages list with a Health and Care Visa due to expire 16/8/22.

I’ve made an ILR application this month but unfortunately priority service was not made available to me at the time. So 6 months.

The catch: I start a new job in a new Trust on the 3/8/22.

I had initially assumed 3c leave meant I could continue working but apparently I didn’t realize if they maybe only meant under the same employer?

Am I going to be in unemployment limbo until they make a decision?