and the decisions over Cole ultimately broke the camel's back and led to Constance M. Burge leaving voluntarily and Kern planning to lay her off (the feeling being mutual). Can this be backed up?

Directly from (https://www.reddit.com/r/charmed/comments/jd3nav/tvtropes_claim_that_brad_kern_created_cole_and/) TVTropes:
Scapegoat Creator: Brad Kern is this for many fans, due to him taking over after creator Constance M Burge left. This is quite ironic, as Burge left over Kern's decision to introduce Cole - who is a fan favorite. Burge gets no backlash for being responsible for the much loathed Piper and Dan romance. Kern is usually blamed for the focus on romance, vampy outfits and a Lighter and Softer tone in the fifth season. If they don't blame him, they blame Alyssa Milano. See I Am Not Spock above.

And this on the Scapegoat Creator (https://tvtropes.org/pmwiki/pmwiki.php/Main/Misblamed?from=Main.ScapegoatCreator) page.

Charmed fans tend to loathe Brad Kern, who took over after Constance M Burge left between Seasons 2 and 3. He tends to be blamed for the Seasonal Rot of later seasons, despite him being responsible for the popular Cole/Phoebe pairing (which is what Burge left the show over in the first place). If you're a fan of the show, how much you loathe Brad Kern will depend on how big a fan you are of Shannen Doherty. Kern fired Doherty due to creative differences (she sided with Burge's vision for the show). Likewise, Alyssa Milano gets rather a lot of hate since the tension between her and Doherty was infamous. Ironically, Constance M Burge gets no hate whatsoever for being the one responsible for >the near-universally despised Piper/Dan romance.

Can anyone verify these claims?