There has been a lot of nonsense about

1. finding a local classical gravity stress-energy density tensor
Pauli's 1921 classic article solves that problem adequately.

2. Newtonian interpretation of Einstein's connection field as

Einstein Connection = Non-inertial Frame Connection Non-Tensor -
Intrinsic Curvature Connection

where

Intrinsic Curvature Connection Tensor =/= 0

In fact

Intrinsic Curvature Connection = 0

and that is one aspect of the equivalence principle i.e.

The local gravity force per unit mass or "g's" felt by a non-geodesic
observer is

g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

For example outside a SSS source, i = 1 is the radial direction

g^1 = GM/r^2

g^2 = g^3 = 0

for static hovering shell non-geodesic LNIF observers at fixed r

Note that g^1 is also the local frame invariant proper acceleration
because {Einstein Connection}^000 = 0.

3. Confusions about potential in GR.

If you look at the SSS metrics

g00 ~ 1 + V(Newton)/c^2

V(Newton) is the classical gravity potential energy per unit test mass.

On the other hand from the local gauge field theory fiber bundle POV

Principle bundle gives the local gauge force field.

Associated bundle gives the source field.

In the standard model, the dynamical symmetry group G is an internal
group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
that the fiber is an internal space, or possibly extra space dimensions
if you use string theory. The source fields are spinor lepton-quarks.
The spacetime symmetry group S is a non-dynamical background.
S =/= G.

On the other hand, in 1916 GR the symmetry group G is the 10-parameter
Poincare space-time group, or possibly the 16-parameter GL(4,R) group
that includes the 15-parameter conformal group of Penrose massless
twistors as a sub-group.

However, in 1916 GR the torsion is zero, this means only the 4-parameter
T4 subgroup of the Poincare group gives dynamically independent degrees
of freedom of the geometrodynamic field that is the fabric of 4D
space-time. The Lorentz group O(1,3) generators are redundant in that limit.

The Diff(4) GCT group is the locally-gauged T4 translation group
generated by total 4-momentum. Since total energy is only conserved if
there is time-translation invariance (Noether's theorem) and since our
accelerating expanding pocket universe in the megaverse of many worlds
is manifestly not time translation invariant in any sense, it is obvious
that the total energy of the universe is not conserved. Our universe is
not a closed system in the classical sense. Indeed, the micro-quantum
zero point vacuum dark energy density at large scale has w = -1
therefore its energy density is constant, therefore the total dark
energy is not conserved.

Now in 1916 GR the geometrodynamic source field is the Cartan mobile
tetrad frame

e^a, a = 0,1,2,3 in local Minkowski tangent space.

The "potential" is the Einstein connection field that is made from
gradients of Newton's potential V(Newton). That is V(Newton) is the
meta-potential of the Einstein Connection potential. This is a unique
feature of the equivalence principle not found in the internal gauge
theories where there is a qualitative separation between the dynamical
group and the space-time group, i.e. S = G is another way to look at the
equivalence principle.