As the Federal Government is responsible for immigration, and to enforce their authority they can stop sanctuary cities
That is the rub...the Feds have failed their responsibility...(if illegals arrive in US cities)...this implies the right of states/cities to deal with the problem like DeSantis and Abbott. If your argument is applied they would be denied any ability to deal with illegals. This gives the left the same "power" to declare sanctuary cities unfortunately.
Border control (federal - under constitutional authority and mandate) is not the same as state policy within state borders (no constitutional federal authority).