> the finding of accelerated expansion on which the dark energy model is based

Dark energy arises because of the decomposition of 4-d spacetime into volumes of 3-d space each distinguishable by a time coordinate, and choosing as the timelike axis the one in which matter is -- on average and at the largest scales -- at rest against the 3-d spatial coordinates.

That fixes a preferred frame -- the cosmological frame -- for observers who are comoving with the spatial coordinates. Such observers will see no dipole anisotropy in the cosmic microwave background (or the cosmic neutrino background, or other relic fields), and will be comfortable with approximating the distribution of visible matter far from them as a homogeneous isotropic fluid, in spite of local inhomogeneities and local anisotropies (like, for example, the planet each of us has between her- or himself and a large percentage of the rest of the universe).

All comoving observers in such a universe will generally agree that in one timelike direction the visible matter is denser and the CMB is hotter and that in the other timelike direction the visible matter is sparser and the CMB is colder. Let's pick the former direction as the past.

All observers in such a universe -- even non-comoving ones -- will agree that it takes energy to separate two massive bodies that are gravitationally bound.

So in the past, when comoving matter was denser, it would take more energy to separate the bits of matter from one another than in the present, when comoving matter is sparser. Something is keeping objects like galaxy clusters fixed against the comoving coordinates, instead of giving them peculiar velocities against these coordinates as they gravitationally attract one another.[1] That is dark energy, and we can experimentally determine its value in the cosmological frame.

The rate at which visible matter is diluting away along the cosmological frame's past->future direction is what what we try to measure.

Standard candles are useful for helping fix a distant galaxy to comoving coordinates. As our confidence in the location of distant matter improves, so does our confidence in the average value of dark energy.
There are a sizable number of relationships involving measurable quantities like angular diameter, surface brightness, emission/absorption line "forests", and so forth that help us fix galaxies in the cosmological frame of reference, so throwing questions upon only one coordinate:observable relationship is far from fatal to our estimates of dark energy density. It sure is interesting though!

So, back to "accelerated expansion": dark energy represents something working against the tendency of matter to gravitatonally collapse. Whether that something is constant or evolves is something we can determine by observation. Whether that something is uniform everywhere outside galaxy clusters or not is also something we can determine by observation.
Current evidence is consistent with a constant uniform feature of the action of large scale structures. In particular, while normally gravitating matter is diluting away in the past->future direction we picked out in our cosmological frame of reference, dark energy is not diluting away.

If, still staying in the cosmological frame, we switch our spatial coordinates from comoving coordinates on the cosmological frame to spherical Earth-centric coordinates, we have to adjust our understanding a little. A distant galaxy has a lower radial distance at earlier times than at later times. We can identify this with a recession velocity, and use that to explain the cosmological redshift and the presence of various cosmological horizons. But this is a coordinate-dependent explanation. It is perfectly fine to stick with comoving coordinates and resort to other explanations for the cosmological redshift.

Indeed, it was that galaxies at extreme distances still look like galaxies that led to the metric expansion of space in the first place: small-angular-diameter galaxy clusters can't really be moving relativistically away from us or they would look VERY different structurally. Additionally, we haven't abandoned Lorentz covariance, so treating matter receding over the horizon as moving superluminally has to be considered a non-physical artifact of a choice of coordinates and frame of reference. And sure enough, just by changing the coordinates alone, these problems disappear.

[1] individual galaxies within a cluster have peculiar velocities against the comoving coordinates that the cluster's centre of momentum stays fixed against. Likewise, massive elements within galaxies (e.g. Earth) have peculiar velocities against the comoving coordinates thanks to local gravitational interactions (e.g. Earth orbits the sun). Each of these introduces an anisotropy in the view of the overall distribution of matter in the universe and in the view of the CMB by an observer with a peculiar velocity. Such observers are not strictly comoving ones. But they're generally awfully close to comoving, because they're almost certainly embedded within a larger structure that is comoving.