An interesting thread, stimulated by a manuscript reviewer's confusion with a paper's conflating "correlation" with the slope in a regression estimation. The posted question prompted a very helpful response that, among other things, deftly explains ANOVA's presence in standard regression output.
"Analysis of variance (ANOVA) is just a technique comparing the variance explained by the model versus the variance not explained by the model. Since regression models have both the explained and unexplained component, it's natural that ANOVA can be applied to them. In many software packages, ANOVA results are routinely reported with linear regression."