Thank you for writing.

Potash or nitrogen-potash is easily  found at garden stores.

You will see three numbers  10 0 10 for example on fertilizers. for Nitrogen, Phosphate, Potash. https://www.ncagr.gov/cyber/kidswrld/plant/label.htm#:~:text=All%20fertilizer%20labels%20have%20three,)%20%2D%20potassium(K))

Most soil here is saturated with phosphate which is harmful to waterways.  

You are looking for something roughly 10-0-50 or 5-0-25 for your garden.
If you tell me the square footage of your garden, I could answer more clearly.

Best to you.

Thank for writing.

That is a beautiful and huge gardent.

You will need 5.5 pounds of nitrogen and 27 pounds of potash. Your soil is depleted this should be applied and thoroughly hoed/tilled in and watered before you plant.  

Your soil report does not give the percent organic material but the soil looks like clay.  Over the long hall, you are going to have to remediate the soil with compost and soil. This will be a big project and I suggest you do it over several seasons. I modified some standard instructions

Adjust the Soil Texture With Organic Material

Proper soil texture is essential to allow roots to take up moisture and air. Dense, clay-type soils can remain too moist, causing roots to drown, while sandy soils can drain too quickly for roots to absorb moisture.

The best way to improve soil texture is by adding organic material, such as compost or peat moss. Decaying organic matter helps sandy soil by retaining water that would otherwise drain away. And it corrects clay soil by making it looser, so air, water, and roots all can penetrate. Plus, in all soils it encourages beneficial microbial activity and provides nutritional benefits.

Common forms of organic material to amend garden soil include:

Tip

An easy test for soil texture is to make a ball of damp garden soil. If it breaks apart easily when you tap it, it's sandy soil. If you can press it between your thumb and finger and make a ribbon, it's clay.

1. Compost: Compost makes an excellent amendment, and it's free if you're composting your garden waste and kitchen scraps.
2. Manure: You often can obtain manure from local farms and stables. It should be composted until it turns dark, crumbly, and odorless. Besides the smell, fresh manure has too much ammonia and can burn your plants.
3. Peat moss: Peat moss is cheap and works well to loosen soil. It's also very dusty, so wet it first to make it easier to work with.
4. Cover crops: Also known as green manure, cover crops are grown on unused soil with the intent of tilling them in and letting them decompose. The roots keep the soil loose, and the plants suppress weeds. Cover crops from the legume family, such as clover and vetch, also add nitrogen to the soil. Cover crops are most often used for vegetable garden sites.
   

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Tips for Improving Garden Soil With Amendments

Adding compost or another organic material is often the easiest way to amend soil. In some cases, a yearly application of compost might eliminate the need for all other forms of amendments. Plant-based composts are lower in salts than those containing decomposed animal manure. These composts are better for improving soil texture, though both do a good job of providing nutrients.

A surface mulch is not a true soil amendment, but it can serve that function if you dig it into the soil once it has broken down. An annual routine of digging in old organic mulch before applying a fresh layer can make for excellent garden soil.

• 
  
  
• Know How to Test the Acidity of Your Soil Without a Pricey Kit
• What Is Organic Matter and What Does It Do for My Garden Soil?
• This Is How to Make Healthy Garden Soil
• 4 Easy Soil Tests You Can Perform Yourself

Now, on to your tomatoes.

Until the entire bed soil is up to grade, plant each tomato plant in at least a quart of potting soil.

Fungus splashes up from overhead watering and rain.  It gets to the lower leaves. At the plant grows, keep it upright and pinch off the lower branches so that no leaf is within 6 inches of the ground. Be sure to mulch around the base of the stem so that dirt is covered.  Your plant in  healthy soil will do much better.  

I hope this helps.

Thanks for writing back Bruno. 
Manure, if not sterilized, can be a problem for home vegetable gardens. https://hort.extension.wisc.edu/articles/safely-using-manure-garden/#:~:text=Many%20vegetable%20gardeners%20swear%20by,vegetables%20and%20cause%20human%20disease 

There are the values of nitrogen and potash in manure ~.5%  Manure is a good soil amendment but is not much of a fertilizer. https://www.allotment-garden.org/composts-fertilisers/npk-nutritional-values-animal-manures-compost/

Tilling/hoeing the fertilizer with the compost is best. Top dress with grass clippings (except if your neighbor is using herbicides or pesticides on  his lawn--then I have no advice) after you plant or seed.  The grass prevents weeds; the compost in the root system holds water.

Write again if you need anything.

Steve