Jupiter and Saturn are brown dwarves, and fit many definitions of "star".
They are both large enough to have developed a hydrogen plasma core furnace that dissolves the rock and ice that was once their core. They are more than just a hydrogen atmosphere, down to the core they're a big ball of plasma undergoing all of the same physics as stellar tissue, except the pressure at the center isn't enough to ignite fusion.
Uranus and Neptune, meanwhile, are likely too small for this, and maintain a fluid ice layer and rocky core beneath their hydrogen envelopes. There is not enough hydrogen for it to take over these worlds. Therefore, they are planets, not brown dwarf stars.
Jupiter and Saturn, however, have grown large enough for the hydrogen to have turned to plasma and dissolved and supplanted their cores with a plasma furnace.
The solar system has three stars. We are not too early to explore other star systems. We know of many planets around Jupiter and Saturn. The extraterrestrial planet with most earth-like atmosphere and surface geology that we know of is Titan, and it's in our neighboring (sub) star system. Huygens and Juice and Europa Clipper and Dragonfly are humanity's first missions to planets around other stars.
Electromagnetically and gravitationally and chemically they act like stars.
Gas giant simulations are often performed by stellar codes such as mesa. Stellar physics and stellar simulations with fusion turned off. Morphologically, they are stars. We should move on from the cold war brain's fusion chauvinism.
They are fundamentally different objects than planets. They have their own planetary systems. They're stars, just unlit.
It seems to be the agreed definition in Astrophysics, that in order for a stellar object to be called "Star" it has to have nuclear fusion.
While a redefiniton would be possible, there is no need and it would just cause confusion.