Stellar variability in Gaia DR3. I. Three-band photometric dispersions for 145 million sources

CONTEXT: The unparalleled characteristics of Gaia photometry make it an excellent choice to study stellar variability. AIMS: To measure the phot. dispersion in G+G_BP+G_RP of the 145 677 450 Gaia DR3 5-parameter sources with G <= 17 mag and G_BP-G_RP with -1.0 to 8.0 mag. To use that unbiased sample to analyze stellar variability in the Milky Way, LMC, and SMC. METHODS: We convert from magnitude uncertainties to the observed phot. dispersions, calculate the instrumental component as a function of apparent magnitude and color, and use it to transform the observed dispersions into the astrophysical ones. We give variability indices in the three bands for the whole sample. We use the subsample of Rimoldini et al. that includes light curves and variability types to calibrate our results and establish their limitations. RESULTS: We use information from the MW, LMC, and SMC CAMDs to discuss variability across the HRD. WDs and sdBs are more variable than MS or RC stars but their variability decreases for the former with age. The MS region in the Gaia CAMD has an s_G distribution peaks at low values (~1-2 mmag) and has a large tail dominated by EBs, RR Lyr stars, and YSOs. RC stars are characterized by little variability, with their s_G distribution peaking at 1 mmag or less. The stars in the PMS region are highly variable, with a power law distribution in s_G with slope 2.75 and a cutoff for values lower than 7 mmag. The luminous red stars region of the Gaia CAMD has the highest variability, with its extreme dominated by AGB stars and with a power law in s_G with a slope of ~2.2 that extends from there to a cutoff of 7 mmag. We show that our method can be used to search for LMC Cepheids. We analyze four stellar clusters with O stars and detect a strong difference in s_G between stars that are already in the MS and those that are still in the PMS. [ABRIDGED BUT NOT TOO FAR]