Hello Andrew. Running out of standard thickeners during a big meal prep session can definitely feel stressful, but you actually have several fantastic alternatives that will keep your dishes rich, stable, and flavorful throughout the week.
For your homestyle vegetable soup, the most reliable and neutral method is to puree a portion of the soup itself. Simply ladle two or three cups of the cooked vegetables and broth into a blender, puree until completely smooth, and stir it back into the pot. Because you are using the ingredients already present in the dish, this will not alter your flavor profile at all, and pureed starches from vegetables like potatoes or carrots hold up exceptionally well to being refrigerated and reheated.
If you want an even thicker base without pureeing your main vegetables, blending a can of drained and rinsed white beans such as cannellini or navy beans into a smooth paste works wonderfully. They have a very mild flavor that easily disappears into the soup while creating a creamy body that will not separate in storage containers.
For your chicken sauce, simple reduction is often the purest approach. Allowing the sauce to simmer gently over medium-low heat without a lid lets excess moisture evaporate naturally, which concentrates the existing flavors and thickens the liquid without adding extra starch.
Another classical option for sauce is finishing it with cold dairy. Taking the pan off the heat and whisking in small cubes of cold, unsalted butter one piece at a time creates a smooth emulsion that adds body and gloss. If your recipe allows for it, a small splash of heavy cream simmered for a few minutes will also provide a stable, luxurious texture that holds together very well during reheating.
I hope these methods help you finish your prep smoothly. Please feel free to ask if you need further clarification on any of the steps.