[carpdad]

What you want to do is common. You will have open crawl space below, so if in a cold region, insulation and air block/seal are important.
My one story expansion. NJ. Town inspector told me. 18" diameter footing and 12" sonotube pier. I think he said every 8' but I used 6' distance and couple of close piers at the corner. Willy nilly diy over engineering. But not many since it was only 14' square or so addition. 36" frost depth and I think 30 psf snow.
Footers don't have to be square like your images. Above is kind of plastic bag form but I used it to show footers can be shaped as such. It can not thin down to nothing. It must have thickness at the edge. I made mine about 12" at center and slope down to about 6" at the perimeter. Used rented one man post hole digger and used long digging stick to dig out the footer hole.
Beam was double 2x10 treated. Floor was 2x10. Bays insulated with r30 fiberglass. I had enough crawl space to add half inch osb from below. Then 1.5 or 2" xps boards and finish with metal lath against mice. I considered closing the space but that invites other problems so left it open. Raised the perimeter ground with 6x6 posts to block rain run off.

 

[carpdad]

Why not draw a plan and ask your local building inspector? Preps for asking needs almost nothing and you may gain a lot. Your plastic footing container is expensive and needs 24" hole which is not really diy. You got 2 options so far, so find out which you can use.
I used footing image because I couldn't easily find monopour pier and footing image. I describe how footing does not have to be nice square box.