If you take two identical plants and put them in containers with all the mineral nutrients they need and then seal them so that one has CO2 while the other does not. both will look the same for a long time. Eventually one will grow while the other one will not. Eventually after months the one without CO2 will die.
If you have enough surface agitation or have enough fish your water can have enough CO2 in it. There is no way to know if you have enough of the CO2 GAS in the tank.
The big problem most people have is the SOLID nutrients that plants need. If just one of the 14 solids is notpressent plants will not grow.. But surprisingly inn those same conditions algae can grow. So So most algae issues are cause by not having enough solid nutrients. Not a lack of CO2.
Compost does have a lot of nutrients rarely balanced nutrient that are gradually get in the water and plants use. How ever compost and plant soils have a limited amount of nutrients so they will eventually run out. You could fix that with fertilizer. But many fertilizers on the market don't have all the nutrients needed or are badly balanced.
In my tank right now I have an inert substrate and and RO water so the only source of nutrients is fertilizer which I make. Since I have started making my fertilizer IEvery plant I have tried has grown very well.
Note the solid nutrients are Nitrogen salts, chloride stays, sulfur salts , Potassium, Calcium, Magnesium, phosphorous, Iron, Manganese, Boron, Zinc, Copper, Molybdenum, and nickel.