Einstein thought of space as a thing. See his 1920 Leyden Address where he said this:
“According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of
space-time, and are partly conditioned by the matter existing outside
of the territory under consideration. This space-time variability of
the reciprocal relations of the standards of space and time, or,
perhaps, the recognition of the fact that 'empty space' in its
physical relation is neither homogeneous nor isotropic, compelling us
to describe its state by ten functions (the gravitation potentials
gμν), has, I think, finally disposed of the view that space
is physically empty”.
He ended by saying this:
"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense,
therefore, there exists an ether".
Also see the Wikipedia aether theories article and note the quote by Robert B Laughlin:
"It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium
when his original premise [in special relativity] was that no such
Laughlin also said space is more like a piece of window glass than ideal Newtonian emptiness. He finished up saying this:
"the modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this
because it is taboo".
Einstein is supposed to have done away with the aether in 1905 but in the end, he didn’t. He thought of space as a something rather than a nothing. In his 1929 essay on the history of field theory, he described a field as a state of space. He was talking about gravitational fields and electromagnetic fields, and said this:
"it can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds".
The point to appreciate is that according to Einstein a field isn’t something that exists in space, it’s a state of space. So yes, space is a thing.