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For example:

  • My shinies from Ultra Sun (random encounters and Ultra Beasts) have star sparkles. However, my shinies from the regular wormholes have square sparkles.
  • My Regis from Omega Ruby (and I believe my Absol too) have star sparkles.
  • My Ramanas Park legendaries and my random encounter Steelix from Brilliant Diamond have star sparkles. However, my Poke Radar Porygon (3 of them) have square sparkles.
    Edit: My Mewtwo from Ramanas Park has Square sparkles.

Basically, what I want to know is what determines the type of sparkles Pokemon transferred from games outside of SWSH have (for example, do specific methods always have certain types of sparkles, if not, is there a base odds)? For this question I mostly want to know Gen 6 and up (I thought I had this in the question but I guess I didn't).

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It's based on personality values.
"For Shiny Pokémon obtained in Generation III, IV, or V, due to the different Shiny rate in those games, there is instead a 7/8 chance of a Shiny Pokémon having star sparkles, and a 1/8 chance of it having square sparkles."
https://bulbapedia.bulbagarden.net/wiki/Shiny_Pok%C3%A9mon#Generation_VIII
If what you've noted is true, you've either had unusual coincidental luck or found evidence that certain met methods/locations/game obtained values are coded to make a certain shiny type. To prove which it is, we'd need a data mine of SW/SH... I'm not sure if there has been one.
I'd be inclined to guess it's just luck—in which case Amethyst is right. Still, this may be worthy of further investigation.
@Mr. Fish is my comment enough for an answer? If not, what other data do you need?
I edited my question with more info that I thought I had. You can have that as part of the answer, but I mostly want to know Gen 6 and up.
I think any shiny obtained in a game with 1/4096 odds will have a 15/16 chance of being a star shiny and a 1/16 chance of being a square shiny when transferred to SwSh. The Bulbapedia article directly mentioning that Gens III-V have a different shiny rate (and thus different sparkle odds) implies that SwSh shares its shiny sparkle determination with other 1/4096 games.
I think that'd be good enough for an answer then, although this does make me want to do more hunting with the PokeRadar when I finish with some other hunts.

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Ordinarily, there is a 15/16 chance of a Shiny Pokémon having a personality value that yields star sparkles, and a 1/16 chance of it having a personality value that yields square sparkles.

For Shiny Pokémon obtained in Generation III, IV, or V, due to the different Shiny rate in those games, there is instead a 7/8 chance of a Shiny Pokémon having star sparkles, and a 1/8 chance of it having square sparkles.

Shiny Pokemon (Bulbapedia)

This implies that generations with 1/4096 shiny rates (VI-IX) have a 15/16 and 1/16 chance of becoming a star or square shiny respectively when transferred to SwSh.

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