Multi-track vehicles are inherently rattlier than bicycles. You're getting shaken on more than one axis. And it's that little bit harder to dodge all the rough bits.
But yes, careful experimentation with tyre pressure is key. Also, trying different kinds of tyres, and occasionally wishing the budget had stretched to suspension
On the basis that barakta doesn't have the hands for dealing with punctures, we started off with Marathon Plus on the baraktacycle, which was as awful as you might expect (and she still managed to get a visitation on the Rea Valley route). I bought some Kojaks to experiment with when they were going cheap, which made her a bit faster (at least on-road), and they had a definite sweet spot for pressure. Then she went electric, so I put a Marathon Plus back on the back (because removing the motor wheel is a right faff) and since rolling resistance was now a non-issue invested in some Big Apples for the front, which were a definite improvement in comfort.
I've seen cycleman make good use of a grippy MTB tyre on the back of his ICE Adventure for silly canal adventures. What it lacked in hawthorn-resistance is made up for with traction on wet bricks.