But I also wonder why you care - is it so that you can keep your job if you don't get the new offer?
If your current company is just a normal company, it might ruffle some feathers. But that company needs you to do the work, so most of the time they’re not just going to fire you for looking somewhere else.
Can you ask someone outside the company for a referral? Most of the time it’s not a key factor in getting hired - they’re just checking a box.
In tech in general "you have no privacy" especially applies to job hunting.
It is dirty and trashy but apparently only some states have it illegal.
References are for HR, hiring managers and back-channel chatter are something else. YMMV.
That seems extremely unprofessional. I wouldn't work at such a place. It seems like a tactic to force you to move.
Look for references outside your employer.
Way back in the mainframe days, we were running compiles and tests down the street at another insurance company. Their data center manager gave me a reference.
Customers and vendors are good.
Once in your second job, you can use previous managers and co-workers.
There were a few employers that called me back to help out in my spare time which I was happy to do.