If 'the narrative' seems to always support the Democrats, it's because that narrative makes the most money via clicks. Is that because more democrats than non democrats read / pay for that content? Who knows. But 'the media ' is not in business to lose money. There is no reason to believe media would support either republicans or democrats. They support anything what earns money.
I would say if there ever was evidence to prove that there is some sort of institutional bias, this would be it. I mean, it's uncanny how lopsided it is, and how often examples occur where the exact same instances and behavior are treated entirely differently, and just happen to drop into the "Democrats = good, Republicans = Bad" narrative.
You're arguing with hard data too. Every study done to gauge the media comes back with numbers that say it's extremely liberal.
There are clearly stories out there to mischaracterize and rattle the cage of Democrats, they just ARE Democrats, so they don't do it. And they hold the keys, so, instead of crapping on their own, they just create "news" to take down who they oppose.
I'd say you're completely naive here. It's not picking narrative over money, they get to have their cake and eat it too.