Fire down on each piece as it passes under the laser and push it back down or slow it down so it drops down.
A focused laser would be even safer. Six smaller lasers that converge on the target but if they miss they spread out again before hitting the atmosphere.

Solar powered and not strong enough to fire all the way to the ground.

This is the key statement. A nation of convict descendants sees a pile of free money and the bureaucrats are clueless but hand it out anyway.
Want to make money in Australia? Form a company, apply for an R&D grant (there are people who write these for a cut which the add to the amount asked for), get grant, rent premises, buy some hardware, pay company directors and engineers (likely the same people) until money runs out, just before a viable product is done and fold company. Rinse, repeat.
Seen it done plenty of times.

Ditto on that thing needing a lot of fuel and maneuvering capability to collect things at speeds that don’t punch a hole in it. The article mentions that they’re hopeful to generate fuel from the metal they catch to fuel metal powered thrusters. OK.

Also please name the thing “Jonah”. Thank you.

Finally, who is going to pay for this? Yes, you took space junk away from near my satellite. No, I’m not paying.

Is there any formal hazard classification of a piece of space junk by orbital velocity, altitude, probability of known orbit crossing, anything like that?

It’s probably enormously complicated and computationally complex to stalk say 10 objects with some kind of common orbital element in order to render some degree of efficiency/cost.

I mean what are you going to do just launch it and wait for some target to present itself because that is not how it works up there.

I hope the company is able to at least get a demonstrator on orbit, but will be a little disappointed if they don’t make a promotional model vaguely shaped like Star Trek’s Planer Killer.