> Noether's Theorem

Right, and we have determined the exact local symmetry with which we can use Noether's Theorem to show a set of exact conservation laws, and expect it to apply everywhere in the universe (and we test against that assiduously).

Concretely, we have ample direct experimental evidence that everywhere accessible in the solar system, to extremely high precision, at length scales of microseconds (and light-microseconds), spacetime has an exact local symmetry group SO(1,3), which is the Poincaré group. The exact symmetries of the Poincaré group include invariance of systems under rotations and translations. Colloquially, it doesn't matter whether your laboratory is laid out east-west vs north-south if you're testing Poincaré invariance wholly within the laboratory, i.e., you're not deliberately testing something much larger, like the Earth's magnetic field, or solar neutrinos, and it doesn't matter if you run your tests in northern hemisphere spring or northern hemisphere winter (notably the planet is at a very different point compared to other solar system bodies at both times, so this is a full spacetime translation).

That is, the results of locally-determinable non-gravitational experiments do not depend on position in spacetime, or orientation with respect to some distant object.

The rotational invariance, via Noether, gives us conservation of angular momentum.

The translation invariance, via Noether, gives us conservation of energy-monentum. With any reasonable splitting of 4-spacetime into three spatial and one timelike dimension, we take the resulting spatial translation invariance and get conservation of linear momentum, and the resulting time translation invariance and get conservation of energy.

In General Relativity, we are guaranteed a patch of flat spacetime around every point in the manifold. Far from massive objects, that patch can cover a fairly large region of spacetime (>> microseconds or light-microseconds). The metric of flat spacetime directly maps to the Poincaré group; more formally, the Poincaré group is the local group theory of Minkowski space, and the Lorentzian metric on the whole spacetime guarantees Minkowski space in small regions.

So even though we must bring in the equivalence principle when doing so, we fully preserve Poincaré invariance at laboratory scales even when on the surface of the various massive bodies in our solar system. This has already been tested experimentally to high precision against several different planetary objects other than the Earth, and several objects which aren't in approximate hydrostatic equilibrium (and thus not planets).

Everywhere we observe (on Earth, elsewhere in the solar system, and with astronomical observations) we see evidence for local Poincaré invariance (up to strong gravity, which is hidden behind event horizons anyway) from emissions and absorptions spectra, and various other observables.

Note, though, that while everywhere-flat spacetime -- the setting of Special Relativity, and in fact what makes the theory Special -- has global Poincaré symmetry, that is not true for spacetime which is not everywhere flat. The global symmetries of the FLRW model of the standard cosmology, for instance, are not time-translation invariant. Therefore there is no correspondence via Noether to a conservation of energy. However, the "swiss-cheese" approach lets us replace a comoving speck of the standard cosmology's expanding dust with a smaller-than-Megaparsec scale region of flat spacetime (corresponding to a region of spacetime far outside any galaxy clusters) or a smaller-than-Megaparsec scale region of Schwarzschild(-like) spacetime (corresponding to a region of spacetime in which there is some collapsing mass, like a galaxy cluster). This is a "sewing" or "stitching-in" process which is described in various places like Misner-Thorne-Wheeler's section on the Israel junction conditions. The standard cosmology gives us a slicing into spatial and timelike dimensions. Thus within in the two examples of "stitched-in" regions, we would the local symmetries in each such spacetime to apply, with appropriately conserved quantities per Noether's Theorem.

Indeed, we test to see whether building up the solar system by sewing together small patches of Schwarzschild(-like) and Minkowski spacetimes accords with the previously mentioned observational tests of General Relativity, at the level of numerical relativity. They do.

So, there is no escaping conservation-of-energy within the solar system theoretically. Tests of the fundamental pieces of this (which are ultimately tests of the equivalence principle under some very light assumptions, and tests of the Standard Model of Particle Physics, which incorporates the Poincaré group directly into it's formalism) support this to many decimal places.

Thus,

> it is constantly violated

is not true anywhere within the solar system, nor anywhere within the local group of galaxies back to when it first started forming stars. That is a rather large volume of spacetime.

However, after one moves sufficiently far away from that region, spacetime is no longer well modelled by a Schwarzschild-like solution, but is instead well-modelled by a Robertson-Walker metric (conversely, within the Milky way, nowhere is space well-modelled by a Robertson-Walker metric). In faraway regions of the universe which matches the observables of Robertson-Walker, one should expect a failure of the global symmetries of Schwarzschild(-like) spacetime.

Finally, even with an expanding Friedmann-Lemaître-Robertson-Walker (FLRW) model, and without "swiss cheese-ing" it, there is still at every point a small patch of spacetime in which the local symmetries are experimentally indistinguishable from Poincaré. Thus, to observe a violation of conservation of momentum (or energy) in our standard expanding spacetime with the observed value for the cosmological constant, you need a separation of millions of lightyears. This is why we see a cosmological redshift from distant galaxies but no cosmological redshift from nearby ones.