Relativistic effects are observed with many other 6th and 7th period elements. For example, the yellow colour of gold and caesium comes from altered electron energy levels due to relativistic orbital contraction, so are the special catalytic and bonding properties of platinum.
OP claimed relativistic effects explain why mercury is liquid at room temperature. That may be part of the story, but it isn't the whole thing, since other heavy elements are not liquid at room temperature.
Explaining relativistic effects in plain text forums to a general audience is a big ask, but here is a link to the first study[0] that gave evidence but it has long expected.
That still doesn't answer why these relativistic effects don't cause neighbouring elements to be liquid. Electron velocities should be quite similar for them. There must be something apart from relativistic effects that makes mercury special in that regard.
Gold is right next door, relativistic effects shrink both Gold and Mercury’s 6s orbitals.
In gold it changes the color, in Mercury it changes freezing temperature.
Gallium has a low melting point 29.76C but that is due to unique chemical bonding.
"relativistic contraction" (shrinking of s and p orbitals) and "relativistic expansion" (destabilization of d and f orbitals) causes many observed phenomena.
Relativistic contraction of the 6s orbital and expansion of the 5d orbital lower the energy required to excite electrons. Consequently, gold absorbs blue light.
Strong relativistic contraction of the outer 6s electrons leaves them tightly bound and unavailable for metallic bonding. This results in incredibly weak atomic interactions, thus mercury a liquid at room temperature.
Lead also has 6s, which is what makes lead acid batteries work as well as they do.
So while the observed effects change, there are relativity effects with several nearby neighbors.
I think you still misunderstood the question. Noone asked if there are relativistic effects with neighbors. In fact, it was said at the very beginning that they certainly have these relativistic effects too. The actual question is why are gold/thallium/cadmium etc. not liquid. There must be something apart from relativistic effects that explains why mercury turns into liquid at room temperature and these others don't.
It also has an effect, it is a small correction in the energies and bounding. Sometimes it's enough to change the color or state, sometimes it's a correction like making it 1% softer or harder and is not interesting unless you are a specialist.
Thanks for the link to the paper published in 2010 (16 years) ago. The OP article from Brown reads as if they were the first to establish importance of Special Relativity for heavy atoms which is not true.
It would be the element underneath it which is synthetic. But it is interesting that all the elements in that row are soft or brittle in pre form or in some compounds.
https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry