What Is Really Conservation Of Energy?

What is the most basic law of physics?
Can we say it is conservation of energy?
Consider the main theories of physics, Quantum Mechanics (micro scale), Relativity (macro scale),
and even Newtonian Mechanics which is highly accurate for human scale (everyday world).
Even though there are known fundamental disagreements between them, aren't they all agree on conservation of energy?
Isn't that show how fundamental conservation of energy is for all physics?
Is there any experiment or observation that breaks it?
On the contrary, whenever an experiment/observation seems to break it at first, assuming it to be still correct leads to solution/progress.
For example Neutrinos were predicted to exist long before they actually detected, just because assuming conservation of energy must always hold.

There are countless highly accurate computer physics simulations today based on QM, Newtonian Mechanics, Relativity.
Aren’t all of them conserve energy?
But is there really such thing as energy in those simulations or what is really conserved is just information?

Are we saying it is theoretically impossible to make a realistic simulation of the Universe(, even if we find TOE someday)?
If we can, would not be everything in that simulation be information, including energy and its conservation?
Many physicists already think Universe could be a computer simulation.
But regardless, Universe is completely mathematical.
(Or we think some things in the Universe cannot be completely described by math?)
Isn’t everything in math just information?
Isn’t that clearly says conservation of energy must be actually conservation of information?