GitLab Community Edition is MIT licensed. I don't know that it gets much more open source than that. I've survived at very very large companies on CE, never needing any of the paid features.
Open core is a business model not a license. You can download GitLab CE and use it under MIT license. You can use all the features it contains and do whatever you want with the code. Yes, GitLab Inc. has other products and some of them are paid, but that doesn't change the fact that GitLab CE is open source.
It's pretty trivial to emulate with a bit of code as a bot and the "conversations must be closed" setting.
But if you're relying on that feature rather than just agreeing, training, and trust, then I'm also not sure that's the best way to go about it. I'd personally much rather be somewhere where the rule is flexible and can be left to the MR submitter to decide when it's important to have more eyes on a change.