Hi there!
Last spring I planted three blueberries shrubs (and I'm planning to add another one or two this year).
When I did I plan them I removed the original soil (rocky clay) and I put back a mix of that clay with manure, organic garden soil, sand and peat moss.

However, this winter I would like to improve it by adding a bit more of sand, peat moss and maybe then covering them with straw, pine needles and cardboard.

My question would be : to add sand and peat moss, is the classical "just on the ground" good enough or would it be necessary to dig a bit around the bush to add it a bit more in depth ?
thans

The sand won't really do anything for them but the peat moss will. If you can scratch it in a little that will help it reach the roots. Acid based fertilizer will help with sweetening the berries as well. I used Epsoma fertilizer when I had my blueberries and they always gave me sweet berries.

Blueberry roots are very fibrous and really like to have good drainage. Sand would only help if drainage is an issue?
Peat moss as mentioned is a great topping.
We do have a clay base on our property but above it is approx 12" of really nice top soil.
Every year in mid to late February we add a topping of peat moss / mulch mostly to insulate the shallow roots from the hot sun.
We have 5 blueberry bushes, all different varieties. As a result we eat and freeze blueberries from late June right into mid september. I have pruned them each year so that they are a long continuous hedge. Also I keep them at a height of no more then 5-6 ft. max.

Up in New England... The wild blueberry shrub doesn't get much more than a foot tall.

Seems like they aren't real particular about nutrients.

https://www.maine.gov/dacf/mna....
Soil and Site Characteristics: Coarse textured glacial outwash deposits form a flat to undulating substrate that can encompass a wide moisture gradient. Xeric conditions on hummocks or raised areas can grade into bog-like vegetation in depressions. Soils are highly acidic and nutrient poor.

In my area... high bush blueberries are found up on the slope where the seep springs are,
What kinds are you planting?

Have you checked with the extension service?
Not finding a lot of information online specific to montana...
Seems like ph level is going to be more important than soil fertility, or removing clay...

Shallow fine fibrous roots, yes, so I avoid scratching around my blueberries. And keep moist. And I'd be careful how much you top dress with sand at one time.
My native soil is acidic. I yearly top with inches of local pine needles that gradually decay, and a little granular fertilizer now and then. Very easy where blueberries and close relatives grow naturally.