What happens if you miss out the final compost layer

by Susan
(Switzerland)

I started out my no-dig garden last autumn with a layer of cardboard, a layer of cow manure and then 10 cm of straw. This was only ligtly covered with garden compost to keep it down. Now the straw did not fly off into neighbouring gardens, but it didn't rot down either. I cannot find any redworms in the mix, the earthworms are plentiful beneath the cardboard, which is soggy but not rotted down.
Is it worth to add garden compost on top now though it is now mid-spring? To what depth?
What about the beds where I have allready planted? I did try to part the straw down to the cardboard so the seedlings sit on the soil, but after a week or so they are starting to look straggly (broad beans, peas).
I also planted potatos in this way and heaped another 10 cm of straw on top, what do I do with them?
Looking forward to all your expert advice,
Susan