We would do all the same experiments we already did (which included sweeping for transmissions), and have the same lack of data that fails to meaningfully distinguish models.
Worse, disproving a hypothesis is not itself evidence in favour of another one unless they're aggressively mutually exclusive - and even then, this is rarely absolute once measurement error/difficulty becomes a factor.
Particularly when you start adding additional items - i.e. unexplained acceleration, okay sure, but how? Either it's something very similar to outgassing (which is what conventional propellants and ion engines are) or it's a new technology we have never encountered, which puts it on worse footing then the more likely explanation of naturally occurring things being observed in an unusual setting (we've never observed an interstellar object before this, haven't after this, it's reasonable to think that the 99.99%+ of it's life it spent outside of the solar system means it starts with surface conditions unlike what we're used to from comets).
But in both cases, starting from the incredible explanation hasn't contributed a way to distinguish the hypotheses - it proposes no new experiments. In fact, generally presuming alien technology artifact shuts down experimental futures: if we're actually being observed by technology, then likely we need do nothing to observe another one - it would be reasonable to expect that aliens are looking for aliens, and will send more probes now that they've found them. Whereas interstellar rocks will require advances in our rocketry and mission staging so we can hopefully find one we can get on an intercept trajectory with.