No, it is MORE broken, because a three level dip is a significant cost.It's less broken than the hexblade/paladin MC.
Not to say that it isn't broken, mutliclassing is an optional rule by default, and I certainly wouldn't allow a hexblade/paladin at my table, but it's less broken than allowing the same benefit without taking the levels.
Which is why you have to be careful using 3rd party stuff. They don't have the same level of QA checks to make sure they can't break the game. WotC would never let a possibility of free CHA-Shillelagh through.Got it via a racial ability and it's almost as much as the race (Dragonkin) gets. They're marginally better than the dragonborn.
Depends what you want to do with it. Battlesmith is the best for hitting stuff. Artillerist is a better party defender due to it's ability to spam temp hp every round, Armorer is a better tank due to it's ability to stop enemies ignoring it. Alchemist is an RP choice, but Tasha's buffs it by making the Homunculus available at level 2, but it depends on how often conditions occur in your game. If you have enemies who spam blindness then the ability to spam lesser restoration is not to be sneezed at.Battlesmith also best the artificer has to offer imho. Two of the subclssses suck imho the other is ok.