This might be better than mathematical constructs which conceivably do not require technology, "just" thought to discover.
The problem here is not even in the need to spend colossal amounts of energy to signal one's presence. The question is whether such advertising is a good idea if the civilization strives to survive; very likely it is not.
There is no reason to believe the symbolic encoding would be the same. For example, if they evolved with 8 fingers instead of 10 they could be driven to encode their symbols in a base 8 system.
I think the point of the OP sharing the PBS spacetime video in this context is that we have reason to believe that the fine structure constant is truly constant throughout the universe. So if the aliens have the capability of measuring and reasoning about electron orbitals and their binding properties with nucleus, then there will likely be significant overlap between our mutual concepts of 'fine-structured-constantness'. Just made that word up. :-)
This would be independent of encoding scheme and independent of practical communication issues.
It's an interesting thought exercise but I don't think there is any reason to expect mathematics to be the same across all potential life in the universe. Human mathematics is adapted to human evolutionary contingencies and the same would be true for alien mathematics, physics, and engineering. By definition of "alien" their mathematics would be alien to us and even if there were commonalities they would be very hard to uncover.
I'm comfortable living with the tension between these two propositions: (1) The manifestation of laws of physics are real, measurable, spread across the galaxies, and essentially outside of our subjective experience. For example, I do believe that gravity and electrons are real ... not just real for me. (2) The way in which we interpret these physical realities is somewhat conditioned by the constraints and experience of being messy human animals.
And I would argue that showing the length of distance we use isn't fundamentally different than explaining which syntax we use for division.
You can dump energy into two frequencies. You're overcomplicating it.
The video suggests binary which is also pretty simple.