TLDR; Don't tell your current employer where you're going. Quit without notice if you will suffer consequences due to not disclosing.
My story from a few years ago:
I gave two weeks notice and informed them where I was going. This manager and team were worthy of this because I respected them and we work in a community so small that employer and employee reputations matter.
One dirtbag (former) manager got upset over yet another defection to one of our largest customers and took specific actions to invalidate my opportunity. How? Our small community made this possible. My departure did not affect Dirtbag. Forget addressing why people are leaving, right?
Malicious Compliance: I was upset so I used Dirtbag's actions and their policy against them. Policy dictates that people are walked out if they are going to a competitor or if they do not disclose their next employer. At one time it appeared that Dirtbag ruined my new job, so I told them that my last day stands because I took another offer. Of course they asked me about my next employer. I declined to answer, citing how this information was used a few days ago. I advised them of what their policy dictates when I do not disclose.
I started sharing with my team members what Dirtbag had done, which helped them be okay with my early departure. I also informed a few important people about Dirtbag's behavior towards our customer. I got my final week as paid time off that didn't count against my earned PTO and I got all my earned PTO cashed out.
They have reached out a few times to hire me back. Dirtbag isn't there anymore. He just slithered into some other job. Life isn't fair and Dirtbag is smart enough to get away with this behavior.
They changed that non-disclosure policy. I just got a referral hire at my company who worked the two week notice period despite not disclosing the new employer. They no longer are trusted or respected enough to get this information.