Both these links mention cell growth during G1 and G2 phase, but not during synthesis phase (only DNA replication is mentioned). Is replication all that happens and is there no cell growth during S phase?
By growth I'm assuming you mean something like an increase in cell mass/volume.
This can likely vary depending on the organism and cell type (biology is riddled with exceptions), but in budding yeast (Saccharomyces cerevisiae) cell mass increases during mitotic S phase1.
The following is a quote from the introduction to reference 1:
Typical pie chart representation of the cell cycle (Figure 1A) stresses the discontinuous events that have to take place only once per cell cycle (i.e., S and M phases), but fails to show that proliferating somatic cells are continuously increasing in their mass throughout the cell cycle (Figure 1B). As pointed out as early as 1971 by Mitchinson2, the “continuous events of the growth cycle” (i.e., increase in cell mass) and the “discontinuous events of the DNA division cycle” (i.e., DNA replication, mitosis, and cell division) need to be tightly coordinated in order to maintain cell size homeostasis.
Main Events That Occur during the Yeast Cell Cycle
(A) General representation of the cell cycle showing the discontinuous events that have to take place only once per cell cycle, namely the S phase and the M phase, spaced with G1 and G2 phases that allow increase of the cell size before DNA replication and cell division, respectively.
(B) During the dynamics of the cell cycle, RNA and proteins increase exponentially, while the DNA content show a typical doubling amount until the cell divides to generate a newborn daughter. From G1 to M phases, the cell increases continuously in mass.