Core component of SQL Server for storing, processing, and securing data
The AI answer gives an outline for how to address this in the realm of SQL 2019. I don't know how accurate the response is, but the idea seems sound, even if it spells kludge.
SQL 2019 is out of mainstream support, so it may be time to think about an upgrade, and with SQL 2025 or SQL 2022 there is a new feature, Contained Availability Groups, which offers new possibilities in this area. A Contained AG has its own master and msdb, which means that when the group fails over, so does master and msdb, and therefore jobs will keep on running.
I will need to add the disclaimer that I have not tested CDC on contained AGs, so I can't say how well it works.