Hackmaster 4th edition is not OSR. Ignoring that it predates the OSR slightly, maybe. It wasn't written to be OSR. It's a retroclone, but it was written as a parody that is also a functional, if ridiculously overwrought, game. Can it run Keep on the Borderlands with minimal conversion? I want to say yes since Keep is for Basic, which includes Holmes basic a simplification of sorts of D&D original flavor. It exists because WotC fucked up and included Knights of the Dinner Table comics a CD. Something they did not have the rights to do. This lead to Jolly Blackburn getting the rights to make direct parody of AD&D and several supplemental products such as Spelljammer. It's a clone from before the idea of making retroclones was a thing. Calling Hackmaster OSR is like saying Palladium Megaversal is OSR, which is a horrible amalgamation of houserules onto AD&D (yest it would harder to run Keep with that but the 1st editon of Palladium Fantasy was much closer to AD&D than the later iterations of Palladium games).
Beyond the Wall isn't a Post-OSR, it's BX with a communal character gen session using prompts, custom classes, and some variant magic. The rules include the classic classes in near identical shape as Basic classes.
Dungeon Crawl Classics being called Post-OSR is weird since it predates several Classic OSR games, while essentially being OSRified 3rd edition. But conceptually, rather than chronologically, it could be viewed as a Post-OSR.
Dark Dungeons is a retro-clone of Rules Cyclopedia with a modification of Spelljammer integrated. Clearly classic OSR.
For Gold & Glory is a retroclone of AD&D, 2e iirc, therefor classic OSR.
I'm not familiar with Mazes & Perils but ad copy says it emulates Holmes basic, so I'd lump it into classic OSR. It likely exists in a similar place as Blueholme, which also clones Holmes but with the notable thing being Journeyman adds content and is published 5 years after MnP, yet is classic OSR. I do own Blueholme and without doing a side-by-side of it with MnP, which I don't own, and Holmes, which I do, I think it's fine as classic. As a side note, I was following BH from when it was first being written a significant time before G+ died.Considering Troika is a retroclone of (Advanced) Fighting Fantasy and was published way back in 2015 and not being able to run Keep without conversions...it makes me wonder what the cut-off for post-OSR and ASR is since I see The Black Hack and Knave under post-OSR but Into the Odd as ASR. This does illustrate the long discussed point on what is OSR and why there is still this discussion.