How can I protect existing fence pickets/rails from raised garden/lawn soil rot

As noted in this answer the only way to slow the rot is to avoid ground contact entirely (Note: Nothing will prevent rot - wood is a natural product and will, when exposed to the elements, eventually turn to dust no matter what protection is applied without continued maintenance, which will be difficult on the portions against dirt.)

You need to minimize/avoid contact between wood and dirt to slow the rot, and that leaves you with a few options:

• Build up the dirt, but slope it down before it gets to the wooden fence
• Build up the dirt within a retaining wall that keeps most of it from the fence
• Cut the bottom of the fence to be ~1" above the dirt
• Take down the fence, build up the dirt, rebuild the fence on top of the new elevation

There is no magic solution to having wood buried in dirt that will prevent/minimize rot. You could have tried some of the old creosote based wood preservatives, but those are highly toxic and have been banned in the US (and probably elsewhere). It was reasonably effective, but no longer available.

You could try a spar/marine varnish on the to-be-burried portion of the fence, but that will be rather expensive and who knows how long it will actually last.

You could just mound the dirt up against the fence, wait for it to rot out, then cut the pickets 1" above the ground once they've rotted out. (Effectively the 3rd option I present, but waiting for rot first instead of cutting first.)

Beyond that, expect accelerated rotting.