Really? Does that mean you've don't believe in the fabled neap tide?
The flood and neap tides are due of course to the tidal fields of the sun and the moon being in alignment, or cross-alignment, respectively.
The article makes no mention of the tidal field of Jupiter et al acting on the sun, but refers instead to the orbit of the sun about the CM of the solar system. This orbit has no dynamic significance for the sun in the way that tidal fields do.
Tidal fields vary as the INVERSE CUBE of the distance, whereas the magnitude of the orbit of a “central body” such as the sun about the CM varies LINEARLY with the distance of a less massive orbiting body. This is a simple “leverage” concept.
You can work it out on “the back of an envelope” that the tidal fields of bodies of the same density vary as the apparent angular diameter. Since the sun and moon have the same apparent angular diameter from the earth, the lesser tidal effect of the sun can be understood as due to its lower density.
Also, the small apparent angular diameter of Jupiter from the sun ( and the earth ) show that it has a small tidal effect, notwithstanding its effect on the CM of the solar system and the “orbit” of the sun.