You’re going to need to compromise or swap around I think.
My Cotic X runs 700×28 Conti GPS on its oe wheels this time of year, ideal for road/town and usable for fire roads, towpaths etc.
I have a second wheelset (Flow 29ers cheap build on 525 from Merlin) that I run Conti CX Race on which are good for mud and dirt but wear fast on tarmac. If you’ve got the new bolt thru fork, options for bargain wheels are going to be reduced.
Something like Schwalbe CX or CX pros are probably a good all round shout. I liked the old wired Maxxis Razes. Lasted about a year of high mileage and coped well with everything from tarmac to mud to snow and ice. Wired X Kings were the worst tyres I ever fitted to this bike although the folding ones are very different.
A set of half decent cx tyres and raise pressures on road, drop on mud/loose is probably the cheapest solution. I tended to drop my Razes to about 40/60 for offroad and go up to 60/80 or so for tarmac.