If the answers to this question are anything to go by, time stop seems to be a surprisingly nuanced spell, but one basic disagreement that's appeared in the comments has been that one camp thinks time stop applies an effect only on the caster, whereas the other thinks it also applies a magical effect to everyone else, too.
Granted, time stop applies a magical effect on the caster - of that, I have no question. But does it also apply a magical effect on everyone else in the multiverse as well?
Why does time stop NOT apply a magical effect on other creatures
Here are the points I've understood for the side that thinks time stop applies only to the caster:
It has a range of Self, meaning that it only applies a magical effect on the caster.
There is no spell in D&D that applies an effect to every single creature in the multiverse, except maybe for wish.
Why DOES time stop apply a magical effect on other creatures
Here are the points from the side that thinks time stop applies a magical effect to everyone as well (I'm a member of this camp):
Spells with a range of Self can still apply magical effects to other creatures, such as detect thoughts, dream, magic jar, and spirit guardians.
The spell's first sentence says: "You briefly stop the flow of time for everyone but yourself," and that wording seems to directly state that everyone but the caster experiences a magical effect where the flow of time stops for them.
There are consequences for choosing one side over the other, which is the motivation for asking this question.
Consequences: Time stop does NOT apply a magical effect to other creatures
Going with the first camp, you can side step the confusion that comes with zones of antimagic and time stop. But, it doesn't strictly follow the wording of the spell by ignoring the sentence "You briefly stop the flow of time for everyone but yourself."
In addition, by claiming that spells with a range of Self do not impose a magical effect on other creatures, that same logic can be applied to, say, magic jar, where a humanoid inside a zone of antimagic can still be possessed because the spell has a range of Self, so it affects only the caster, and therefore the possession of other creatures is not a magical effect of the spell. The same logic can be applied to many other spells with a range of Self, some of which are listed above.
Consequences: Time stop DOES apply a magical effect to other creatures
Going with the second camp, yes, you can more closely follow the spell's text as written. However, you also open the doors to the aforementioned confusion between zones of antimagic and time stop.
If time stop creates a magical effect on every other creature in the multiverse, across planes of existence (which seems to be the valid interpretation of "everyone but yourself" - and take note, this is a 9th level spell on par with wish), then being immune to it in any way (whether you're inside a zone of antimagic, you are immune via the wish spell, or you're one of the gods of the multiverse) will allow you to observe as everyone suddenly freezes in time whenever someone casts time stop.
It also fails to offer a resolution to the linked question, where initiative order between someone inside an antimagic field and a caster of time stop is not well defined.
With all the above in context, the question is as the title says: does Time Stop apply a magical effect on only the caster, or does it affect everyone else too?