Dirt not soil

In my other thread I have built 4 raised beds, internally 1mtr x 2.4
I had 2 tons of topsoil delivered, which has put 2 beds into use  no 3 is not filled enough yet and no 4 is going to be a compost bin for turf when I get to it.
I bought the top soil understanding that it would not be the best quality but could be improved
I tested it today at a pH level of between 6.5 and 7, I want to improve its overall health
I'm confused as to what to add
Currently locally I could get peat compost, mushroom compost or coco coir?
The topsoil is very grey when dry and quite heavy

Any suggestions?
Ta Ray

I'd add that I would personally not go for the peat based stuff, I'm no eco warrior but peat is a resource we really shouldn't be using these days, even if it is fantastic for growing in. Mushroom all the way!