I've just recently learned that BGP runs at the application layer (with some criticism towards that), and on Autonomous Systems only (with strict configuration and rules), which apparently according to some searching around almost always means ISP routers.
To my understanding of what constitutes a router and packet forwarding, that basically excludes SOHO routers from running BGP. Is that conclusion correct? And do SOHO routers just forward any packets going out of the network immediately to the ISP in that case?