If we build heavy Casimir plates near a Cavendish experiment, the latter will point to the former as a normal gravitational source. Rather than claiming that there is a tiny Cavendish apparatus deviation for heavy Casimir plates held close together and in parallel vs the same plates with a different orientation or separation, one should really show it in a lab.

(One might also try to use a Casimir setup to lift some heavy object off the floor, or do other gravimetry experiments).

The usual explanation for the Casimir results involves modes in the fields of the Standard Model, all of which couple in the same way to the curvature of spacetime.

In the language of particles and charges (which we conventionally get to by considering the spin statistics of gravitational waves in General Relativity), all the Standard Model particles have the same gravitational charge. That includes everything involved in a Casimir experiment, including "vacuum energy" if any.

However, so far most of the thought that has gone into "how do we scatter matter around flat spacetime to induce an Alcubierre metric on it" requires stuff with the opposite gravitational charge.

Back to the language of metric theories of gravitation: if there is only one gravitational charge that everything possesses, then everything couples to a single metric tensor. If we allow for a gravitational charge that has both positive and negative signs, so far as we know (from among other things analysis under the PPNF[1]) we are forced (by the Universality of Free Fall) into having matter couple to a metric tensor according to the sign of its charge. This is what we would call a bimetric theory of gravity, and such theories have been studied for decades motivated by understanding the very early universe https://en.wikipedia.org/wiki/Bimetric_gravity

Generically, one asks "where's all the stuff that falls differently?" and almost inevitably has to say "it fell out of our universe much earlier than the formation of the cosmic microwave background, or decayed into ordinary stuff, or dilute away much faster during the metric expansion than ordinary stuff and became undetectably sparse before the first stars shone", or in other words that either the second metric tensor has decayed to all zeroes everywhere in the observable universe, or that nothing is in the observable universe that couples to it. Otherwise there are lots and lots of bullets to bite about why we don't see any observables that would support the second metric.

Alcubierre's "drive" paper (he has left a copy at https://arxiv.org/abs/gr-qc/0009013v1 ) uses one metric, not two. The warp bubble is also eternal. Importing a whole extra metric tensor into our fundamental theory of gravity is a really high price to pay for having a mechanism which can produce a non-eternal warp bubble (one that forms in the finite past and un-forms in the finite future). And then one has to really spread around a lot of matter that couples with (i.e., it sources as well as follows) the second metric if one hopes to steer the warp bubble. We probably end up in some ratholes of inventing entire chemistries and nuclear physics of "negatively gravitationally charged" matter, and then figure out how it interacts with normal matter when they're confined together in some system.

So although a terse "well maybe it's hiding in the Casimir effect" massively underplays what is needed, or what the consequences would be of reproducible Cavendish (or other gravimeter) experiments on Casimir apparatuses that show that when the plates are being drawn together they are also lighter (in a weight-is-the-quantity-that-bathroom-scales-measure sense). Show it happens at all first, even if it's a very very weak effect, then take seriously thoughts about scaling it up.

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[1] PPNF, or PPN formalism: https://en.wikipedia.org/wiki/Parameterized_post-Newtonian_f...