Didn't realize my current company is part of the same Private Equity Firm as the job I applied to, and now I need to tell my current employer I'm searching or else the Firm will do it for me...help!

I have been applying for new opportunities for a few months, and one of them recently sent me the next steps (after resume/application review), which was one of those online personality assessments/general IQ/aptitude test, but it was done via ProctorU so I would not need to retake the test in a controlled environment to prove I wasn't cheating in the future. I apparently got a good score, as I received an email that they next wanted to do a phone screen.

One issue though: Apparently my company is owned/managed by the same Private Equity firm as the job I applied for, and unbeknownst to me the firm has a policy of contacting an applicant's current employer if the current employer is a part of it's portfolio. Luckily they have not done so already, but the HR manager reached out asking for permission, and to inform me that would be the first step needed to be done before I could continue with my application.

What is everyone's advice in this situation? Now obviously one is advised not to tell their current employer they are looking in normal situations, and I guess also to not apply for jobs like this (same PE Firm with this policy), but I'm still not sure my best course of action. Should I give up on this offer? I am not yet old/advanced enough where I can guarantee I either find a job quickly (if my current employer were to let me go if they found out about this), or almost certainly get this job if I continue with the application. Any chance that their notification method isn't just some like electronic "mark my employee account that I'm searching for jobs" but my manager wouldn't find out unless he went looking for it? I am fairly certain I wouldn't at least be let go/HR looking for reasons to let me go until after the holidays (when I'd hopefully either have this role or another role that isn't affected by this issue I'm currently interviewing for) because it's our busy season and they frankly need my manpower/workload management until the new year.

Thanks, and let me know if anyone needs more clarification to give me better advice etc!

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