Framework 13 AMD won't steadily charge with Anker 67W compact wall charger when anything else is plugged into it

Sure sounds like a power distribution problem with the charger.
May be linked to this issue. AMD Framework USB-C charger compatibility issues - #36 by patagona

To be clear, I don’t mean a PD issue, I mean an issue with the charger distributing power among it’s ports. From what I’ve seen most chargers will split power to the ports regardless of a load being hooked up, so a USB cable with nothing on it will drop your output on all ports and force a renogotiate. IIRC iphones had some problems with this in recent versions.