It sort of can but all non-adobe software I know of, even commercial stuff like Affinity Photo, has spotty support for some PSD features.

Basically any given PSD will certainly load correctly in photoshop, but you're rolling the dice if you want to load it into anything else. More so if you are using more modern features.

For InDesign magazines with embedded images, for example, I'm not aware of any compatible 3rd party software

Here are some options which might help [0] (Bias: I love Affinity Publisher and despise Adobe).

0 - https://forum.affinity.serif.com/index.php?/topic/225143-wha...

If not, Affinity Photo or Photopea will probably do the job.