Of course Alito and Thomas would have allowed the government unlimited power. I am bit surprised to see Barret in the minority of this one.
As per the current conservative trend of allowing authoritarianism through technicality, the majority of Alito's dissent is just that the Court shouldn't rule on this at all because it won't help the defendant's case much specifically.
She's not as big on some of the broader interpretations of the 4th amendment that more civil liberty minded justices would lend credence to.