Are these eggs safe to eat? I like to hard boil eggs because they are one of very few foods that help when my sugar levels are too low.

But now Im a little paranoid. The other week I read online that if you take an egg out of the refrigerator and shake it, if you can feel stuff moving around inside then its not safe to eat.

I just did that with all 12 eggs I have and according to what I read, they're all bad.

But the usedby date on the carton says 21 August. So, are they safe to eat? How else can I determine if they are safe to eat without cracking the shell and without boiling it first?
I have heard it stated before, but here it is from various sources:

Source 1

Source 2 (confirms the shake test)

Source 3

In general, the air pocket in an egg gets bigger as it gets older due to the permeability of the shell.  I think the shake test is a little hinky, unless it actually sounds like water sloshing.  I would try the float test; fill a bowl to twice the height of the egg, and place it in.  If it sinks to its side, it's fresh.  If it stands on its end, it's probably good, but needs to be used quickly.  If it floats, toss it.