Q.Why Are My Sun Flowers Rotting Away?
This is my second attempt to grow sunflowers in pots. I thought it was slugs that was eating / devouring my sun flowers, yet, I see little or no evidence that my slug pellets. Do I (I’m now thinking) have a fungus or disease eatinf at my plants? Please help – I am an absolute beginner to this.

Certified GKH Gardening Expert
I can't get a good look at the soil, but this does appear to be diseased. Usually, this happens with soils that don't have a chance to dry out between waterings.
I would start fresh. Container, and all. You can attempt to sterilize that one, but it may come with many more attempts before it DOES get sterilized. Better to use a fresh pot and fresh soil. Be mindful to let it dry out between waterings, and don't feed if there is already feed present in soil.
After all of these adjustments are made, your sunflowers should do quite well. They don't seem to mind container life, and grow just find in pot.
Here are some articles that will help:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/improving-garden-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/macro-and-micro-elements.htm
https://www.gardeningknowhow.com/ornamental/flowers/sunflower/caring-for-potted-sunflowers.htm