Although it's great that it's provoked you into asking questions, it seems like there is a lot that the PBS video must not be placing into your mind, like how these asteroid size masses are moving with respect to some local standard of rest in their region of the galaxy (and how commonplace they are) are crucial to the idea.

If they're moving gently along with all the stars in their neighbourhood, collisions between these asteroid-mass black holes and anything appreciable is unlikely (just as star-star collisions are very rare) that we wouldn't expect to see that ever happen.

Wandering pretty violently in comparison to nearby bright objects, an asteroid-sized black hole is likely to zip by a star and its satellites on a (strongly) hyperbolic orbit, like <https://en.wikipedia.org/wiki/%CA%BBOumuamua>, just dimmer. It's even less likely to hit a neutron star because of the NS's compactness, and because the geodesics it generates produces greater hyperbolicity near its surface (because that's quite near the centre of mass) than near the surface of a regular star. And hitting a sun-like star is already hard for an asteroid: <http://curious.astro.cornell.edu/our-solar-system/comets-met...> (likewise, we have never seen a small black hole flare up near our sun).

It is more likely that -- very occasionally -- an asteroid mass object (by strong equivalence principle, it does not matter if it is rocky, icy, or a black hole) is captured into a weakly hyperbolic orbit, or even an elliptical one, by a ~stellar mass. There are reasons to think an NS might be more efficient at this than a fatter star. But then you get a (possibly wide) binary star-BH that soon becomes hard to distinguish from a binary that formed together and "grew up" as stars together, with one happening to get too fat and collapse. The missing nebula in the captured-BH case would raise questions.

I don't buy the idea of a small black hole that somehow manages to slice through a neutron star doing much to the neutron star. Typically many many solar masses of matter fall back onto neutron stars after they violently form, and almost certainly there are asteroid-sized chunks of heavy atomic nuclei landing on them often. If you had some cosmic pool shark aim a small BH so precisely that it not only enters the (very very very very very small) NS core, but stays there, coming to a stop just so, the NS would collapse into the BH [1], because no matter can rest just outside the event horizon. The inner hard "platform" matter would fall in first, and in turn the freshly unsupported upper layers which had been "standing" on that platform would fall in, and so on down the widening drain. But if you shoot an asteroid-mass through an NS, it's hard to think there'd be much consequence. Sufficently slowly, there could be a nuclear explosion but probably not one that's catastrophic to the NS's integrity: I think it'd be hard to distinguish from the nuclear explosions from the rain of supernova-remnant material falling back down onto it, or random interstellar matter an isolated NS might encounter, or crustal quakes.

(I could be convinced by an academic paper equipped with an NS equation of state though (see [1] again), in principle, but very likely not a youtube video, much less a second-hand summary of one :-) ).

To a zeroth order approximation, the effect on a planet of a collision with an asteroid-mass black hole is not going to too different from the effect of a pair of collisions with ordinary asteroids (the "pair" is from the ingress and egress sides of the "tunnel": actual asteroids will tend hit a surface and stay there, or break up in a thick planetary atmosphere if there is one, etc., while small black holes will sail through). The asteroid-mass black hole will certainly create lots of electromagnetic interaction on contact; you can think of how black holes tend to have bright accretion structures, so you expect a big flashy kaboom as with a rock (but with more X-rays and gammas).

While we can resolve exoplanets, we can't quite see them being hit by asteroids, assuming the Jupiter-type exoplanets are hit with some frequency, we could blame limits in our telescopes. (JWST will help very soon!). Rockier exoplanets are no more likely to be hit by asteroids and lit up brightly than Earth or Mars. Asteroids are just tiny masses compared to these bodies.

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[1] fate of a neutron star with an "endoparasitic" small (and possibly primordial) black hole, that "just so" is already inside the NS: https://arxiv.org/abs/2101.12220