Creating a better looking trampoline area in your garden

With regards to your question on the trampoline and creating a better looking area

I would dig out to about 50mm under the trampoline add landscape weed sheeting then cover with a good quality bark ( not wood chips as this will blow over the garden in the summer when it dries our.
Here are some links
https://www.toolstation.com/heavy-duty-landscape-fabric/p45800
https://www.diy.com/departments/verve-dark-brown-bark-chippings-large-100l-bag/1586186_BQ.prd

Finally You could add some fern plants just on the edge around the front of the trampoline as its the perfect place for them in the shade just under the trampoline

Here are some ferns that are well-suited to growing in shaded areas in the UK:Hart’s tongue fern (Asplenium scolopendrium)Lady fern (Athyrium filix-femina)Soft shield fern (Polystichum setiferum)Male fern (Dryopteris filix-mas)Shuttlecock fern (Matteuccia struthiopteris)Royal fern (Osmunda regalis)Hard fern (Blechnum spicant)Maidenhair spleenwort (Asplenium trichomanes)
All of these ferns prefer moist, well-draining soil and will thrive in a shaded area.

The soil you dig out might be useful to create a top dressing for the lawn