The proposal here is very similar to the Breakthrough Starshot initiative that wants to send a probe to Alpha Centauri, the nearest star system to our sun.
Basically the idea is to take a very small (i.e. low mass) craft with a large solar sail and accelerate it to a significant fraction of the speed of light using very powerful ground-based microwave laser arrays. The neat thing about this concept is that all of the technology essentially exists already — it's just a matter of scaling up existing concepts and miniaturizing existing sensors.
The black hole rendezvous suggested in this paper is a lot more ambitious than Starshot, targeting a distance of 20-40 light-years (for comparison Alpha Centauri is only about 4 light-years away) and a max speed of 30% the speed of light (vs a speed of ~10% c targeted by Starshot). I think the main problem here (other than the requirement of building what essentially amounts to a microwave death ray) would be developing an antenna that's both small enough to fit under the strict mass limits and powerful enough to broadcast the data 20+ light-years back to Earth. Maybe space-time lensing effects around the black hole itself could be used to amplify the signal? Another problem is that even at extreme speeds, this is a multi-decade mission — like 70+ years. Considering the travel delay involved in sending back a signal, it'll be a century at least before any data would arrive at Earth. Unfortunately, century-long projects are an extremely hard sell for the people who hold the scientific purse strings.
Oh, also... We don't currently know of any BHs within the target range, and the paper's author even admits that any targets more distant than 50ish light-years are basically unreachable. The current closest-known BH is more than 1000 light-years away, so we've still got a lot of work to do in finding a suitable target. Fortunately the field of black hole detection is advancing quickly, and the new Vera Rubin observatory is very likely to spot many previously-unknown black holes in the coming years. Hopefully some of those will be close!