I never understood why you would use a big pot with "filler" (not soil)..if the plants are growing in less soil why not use a smaller pot?..

Even cheaper and simpler would be to grow in the ground using your native soil. Maybe next year? You could use that area where you've put down the fabric. It will have killed off the grass. You'll just need to dig it over and plant.

A single indeterminate tomato will fill one of those large pots easily! And the roots will need all that room so nothing but potting soil, please.

IME with many years of container gardening, the more shortcuts you take and the more you try to cut costs on the potting mix, the less successful your growing experience will be.

I have grown patty pan squash in a container like that. It will benefit from some sort of trellising : a tomato cage or some sort of homemade construction will work fine.

If you are on a budget, maybe take a look at Craigslist or Freecycle or Nextdoor (if you have that app in your area). You may be able to find someone who wants to get rid of some for free or very cheap.

Filling the bottom with sticks would just cause nitrogen deficiency because the bacteria that breaks down the sticks ties up the nitrogen.

The cheapest soilless medium is going to be in bulk from a local landscape supply company. Delivery can be expensive but if you have a pickup or can get one cheap (4 hr rentals aren't too bad), you can go pick up a scoop.

Least expensive is growing in the ground.