The pointed pattern means she almost certainly had some Siamese ancestors on both sides, but it doesn't tell anything about how recent they were. She doesn't look from that photo like she has much Siamese in her (but it sounds like she acts like one!)
It's very unusual that we can tell from a coat color or pattern that a cat probably has some particular breed in them. but the pointed pattern is an exception, since it actually came from the Siamese into other breeds and into the general cat populations in other countries. It is not native to Western countries. and was not known in those countries at the time Siamese cats first were being brought to Europe. But over the past ca. 130 years, due to Siamese cats and their descendents mating with the local cats, the pointed gene has been widely spread throughout the random-bred cat populations in countries to which the Siamese have been imported. It's a recessive gene so it can be hidden for generations until 2 cats who carry it happen to mate and both give a copy to a kitten.
Anyway, there are now many pointed moggies, and most probably have very little Siamese in them. A lot of the mixing no doubt happened in the mid 20th century when Siamese were at their height of popularity and at that time many people had unaltered, indoor-outdoor pet cats including pedigreed cats. It would be less common today when there is more spay/neuter and it can be done at an early age, so many breeders have pet kittens altered before going to new homes. and people are more likely to keep their pet Siamese indoors or in a secure outdoor enclosure But it's still a popular breed, and there are irresponsible people, so there are still some mixes being born with a Siamese parent.
But the majority of random-bred pointed cats are probably far more Western moggy than Siamese, so really it's more a pointed domestic. If a cat has distinctive Siamese traits (like long, lithe body, pronounced pointed muzzle, unusual voice, and some typical personality traits) .enough that it seems like the cat had a recent Siamese ancestor , then I would think of it as a (probable) Siamese mix. And a few could be actual Siamese. I think the coat is a crucial factor. There are Siamese mixes who have the above , but it seems they very seldom get the real Siamese coat. A real Siamese has a short single coat that lies close to the body, with no undercoat like Western domestic shorthairs and domestic longhairs have. And it's usually shorter than a Western DSH's coat. The shortness plus no undercoat means it sort of looks like there are "seams" in some places where the fur meets growing in 2 different directions
Hope you find a great home for this girl. If I were just speaking personally just based on the photo I would call the cat a pointed moggy. But if I were listing her for a rescue or shelter and it would help her get a home, then SURE I would call her a Siamese mix. It's technically true, anyway, even if the mix may be <1% Siamese / >99% Domestic.
