There is no reason to expect that any 4D Universe even has protons and electrons, the basic fields, etc. So all the fictional physics we imagine here is just an intellectual exercise. Mathematicians stick to geometric figures which have the advantage of being imaginary. But there is only so much you can do with those. I want more so I'll assume elementary particles and fields but exclude the dubious idea of atoms. Can you have life without atoms? No one knows, but I like to think yes.

A hobby of mine has been the physics of neutron star cores. In particular I followed the works of Egor Babaev, https://en.wikipedia.org/wiki/Egor_Babaev who has all the credentials you could ask for and a great many publications in the most prestigious journals. So while this physics is scarcely known even to physicists it is quite well established.

The core of a neutron star is a place where quantum effects dominate. It is both a neutron superfluid and a proton superconductor. (With pressure so extreme one can have superconductivity at a billion Kelvin.) As a superfluid the core is shot through with a great many impenetrable rotational vortices, each with one quantum of rotational energy. The core is similarly shot through with even more electromagnetic vortices, each with one quantum of electromagnetic energy. Both of these vortices go in a roughly straight line from the surface of the core to the more or less opposite surface. The superconductor is of type 1.5. This means that these electromagnetic vortices [evortices] will tend to form small groups of one through nine evortices. Such groups are stabilized by their quantum nature. Each vortex has only a fractional quantum of energy. The difference is made up by a supervortex shared by all the members of the group. The result is called a polygonal vortex, which must have a whole number of quanta. Such a group with four evortices is called a square vortex, and so forth.

It is further calculated that these polygonal vortices will be twisted due to the rotation of the star. To relieve their twisting, toroidal twisted vortices will tend to pinch off from a vortex. Take a string and twist it : once it is twisted enough it will start to develop lumps. In an evortex these can pinch off to form a tiny twisted torus. It seems that the whole group will pinch off. So we would get ten types of torus, depending on the number of evortices in the group.

So far this is generally accepted even though it's all based on calculations. I can't imagine how a confirming experiments could be done here on Earth. It seems impossible to produce the necessary pressures, so extreme that the neutrons are on the verge of forming a quark plasma or even a black hole. So exact numbers are not available. From this point on I'm going to be speculating.

We know that atoms can combine to form all sorts of things, even living ones. What I'm looking for is for an analog of atoms. Requirements are stability, a certain amount of variety, and unlimited ability to combine into more complex things that may be stable or unstable. Could these torioids fill the bill? No one knows, but it seems possible. If so, then it seems that life could evolve in neutron star cores.

Rather to my surprise I was not the first to consider the possibility of life evolving in the core of a neutron star. This honor goes to a teenaged Anders Sandberg, now a a senior research fellow at the Future of Humanity Institute at the University of Oxford. He published the idea as science fictional Hildemar's Knots. https://www.orionsarm.com/eg-article/46709d53449d2. At the time polygonal vortices had not been conceived of, so he got the requisite variety by having the vortices form the closed curves which mathematicians call knots. This won't work in 4D, but as we've seen polygonal vortices provide the requisite variety so we don't need that.