This is just a guess, but how about the concentration of some intracellular signalling molecule?

If a cell has a baseline production of some such protein, it would then stop synthesizing cell membrane when the concentration of that molecule falls below a level that would trigger the synthesis. So there’d be a some kind of feedback system for cell membrane and/or cytoskeleton production. Of course, the eventual size of the cell would then depend on the baseline activity of the gene for the signalling protein in question.

How does that sound?

I also vaguely remember reading somewhere that certain especially big cells (such as eggs) are so large because they have several copies of genes that affect the cell size by synthesizing more substance for the cell. How this works in practice and how the final cell size is determined, I don’t remember.

I think it’s concentration of cAMP. I agree with the above explanation. Feedback loops seem logical… This is based on that when you culture something in a petri dish, it will stop growing, like e. coli. The chemical messenger that tells cells that there is no room and they need to stop dividing, in this case, is cAMP. Based on that, I would think that it is similar in regulating its individual size.

agree with MrMystery re. simple explanation of cAMP and dispute that a volume/surface area mathematical limit is effectively the control element. Coenocytic fungi are effectively huge continuous cells (with no crosswalls) as are some life stages of so-called slime molds.