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I wouldn't get your hopes up for the legendaries.
The box art legendaries have been shiny locked since gen 5.
As for starters, in SwSh and Legends the inital gift ones are shiny locked, but additional ones bred or caught later aren't. You should be able to breed for them at the very least.
Yeah, I don't expect legendaries to be shiny huntable, but starters for sure! If only I had patience to keep doing it but I'd be too tempted to play right away, especially with everyone around me playing. Maybe I'll shiny hunt Sprigatito via breeding instead.