Note that both points you quote for being on topic specifically mention "engineering". Engineering is about applying the laws of physics and other sciences to real world problems.
Science seeks to describe how nature works by applying observation, logical deduction, and experimental verification. Personal beliefs have no place, other than perhaps to guide a scientist what to investigate next.
Religion, on the other hand, is specifically about beliefs that are held to be true solely because they are believed to be true. Note the circular reasoning here. That's invalid logic, so is invalid science. As invalid science, it has no bearing on engineering.
So the answer to your statement about "I do not see anything there about anything religious" is that it is implied in "engineering". Engineering relies on science, which relies on valid logic to reach conclusions. Religion is not founded on valid logic, so you might say it is inadmissible as evidence and irrelevant to engineering.
Problems with your particular question:
As recorded in Genesis 11:1-9 ...
By starting out with a religious reference, you lost any benefit of the doubt about this being about engineering. You now have the burden to show it's NOT about religion.
According to the sources brought in this question and this one, both at Mi Yodeya
This is just a waste of space. Worse, it seems you think this is a source (of what exactly?) somehow, like you would quote in a scientific paper. Remember, the arbitrary beliefs of others have no bearing in engineering.
its height are given as 2.6 km, 5 km, 52.5 km, or 138.24 km
This is way over the top, and totally impeaches your question. Clearly anything built by ancients of bricks wasn't 2600 meters tall. You don't have to know much science for that. Even if maybe you thought that was borderline feasible, 140 km is just grossly absurd. These figures are so out of line that this question is clearly about fantasy, not engineering.
Reading the rest of the question is pointless after this.
If you really just wanted to know about the height limits of a free standing structure people could have built 3800 years ago, you could have asked that without any references to religion at all. Why does it matter that there is a vague reference to a tower in a compilation of religious beliefs? Why even bring up that in a particular fantasy there was a tower 138.24 km (5 decimal places!) tall?
These issues were pointed out to you in comments, but you refused to fix the question. That indicates that the religious references are somehow important to your question, which means it doesn't belong here. It was downvoted for good reason, and it should be closed.
This did get me curious about height limits of such structures, so I asked the question Height limits of brick and mortar tower?. Note the lack of religious references.
If a question is truly about engineering, then it doesn't need references to anyone's unfounded beliefs. Therefore, such references should be omitted. If they are included, then it's a strong hint that the question is not about engineering, and is off topic on this site.