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There have been many questions this year about plants not blooming. One has to wonder if weather has something to do with it. The first thing that comes to mind for you is the pot. This fall or next spring, slide the rhizome out of the pot. It may be too large for the pot at this point or the potting mix, which deteriorates, may need to be replaced. It is hard to keep roots from over-heating in pots when plants need full sun. Perhaps avoiding terra cotta and pots with dark glazes will help. Mulch the top to lessen sunlight/heat to the soil and help maintain consistent soil moisture. Try a fertilizer with less nitrogen than the one you are currently using. e.g. instead of 10-10-10, try 4-10-4. I've included an article on dividing calla lily. https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/dividing-calla-lilies.htm

I dig up my calla lily before frost hits. Remove the foliage as close as you can to the tuber (use a knife); clip the roots short; and gently brush off any soil. Cut out any soft spots or off-colored areas. It should air out of the sun for 5 days before going into storage. Sawdust, peat moss or vermiculite all work for storing bulbs as long as the container is cardboard. I wrap mine in newspaper, put them into a mesh bag similar to what 5 pounds of fruit come in and hang it up in a cool, dark place. In spring after the soil has warmed to 15C, prepare your planting area. Dig in several inches of sphagnum peat moss and compost and an appropriate amount of long-acting fertilizer. Calla lilies must have lots of sun and consistently moist soil to bloom freely. Make sure other growing plants aren't shading your calla. Long-acting fertilizer often doesn't last through the growing season. If growth seems to slow (or blooms stop) switch to liquid fertilizer in July/August. Here are articles with more tips. https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/growing-calla-lilies-and-care-of-calla-lilies.htm
https://www.gardeningknowhow.com/ornamental/bulbs/bgen/preparing-bulbs-for-winter-how-to-store-bulbs-for-winter.htm

That is a seed pod. Growing seed from a hybrid plant is sometimes disappointing because the resultant plant doesn't have the same genetics as the parent. You never know so give it a try. Here is how: https://www.gardeningknowhow.com/.../calla-lily/calla-lily-seed-info.htm

Calla lily seeds form in the center of the flower if it is pollinated. Since you seem to be growing a hybrid, seed-produced plants will not look exactly like the parent plant. As with all seed collecting, make sure it is fully developed and dried. Information on growing calla from seed in in the following article:
https://www.gardeningknowhow.com/.../calla-lily/calla-lily-seed-info.htm

You could, definitely, divide it. There would be no harm in this, and it is a good way to make more plants! Here is an article that will help: https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/dividing-calla-lilies.htm