ZDoom

Can't fit everything in title.

In hub levels, the player will not follow player start angles when entering a level. Instead, the player will spawn into the new level facing whichever angle they were in from the previous level.

Works for me. Keep in mind that this is a parameter of Teleport_NewMap.
I tested it with Hexen which doesn't preserve the angle and with Strife which does.

Both worked correctly. So please post a runnable example where you think it is wrong.

Here, example file. Supposedly in non-level-refactor version, the player will snap to the player start angles on the new map.

You omitted the crucial bit of info that this only happens when using ChangeLevel with a certain combination of flags. That's why it worked in Hexen and not in your demo.