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There are 2 Pokedex books out there that ONLY include Pokemon without any strategy stuff, those being ORAS and the USUM Nat Dex books. I know the comparison between the Nat & Region Dex isn't that great, but that's the only way we can measure it as accurate as possible.
XY & LGPE were the only Pokedex books to include 1 FORM of Pokemon per page and mixed in a strategy guide as well, so I can't use those.
ORAS national dex had 592 pages, with 2 FORMS of Pokemon occupying 1 page and 767 forms of Pokemon to cover (megas included). With Vivillon's form in mind, it took 384 pages to include all the Pokemon as the remaining pages were used to include items and moves. This makes ~65% of the book being dedicated to the Pokedex.
USUM national dex had 720 pages, with 2 FORMS of Pokemon occupying 1 page as well, leaving us with a total of 855 FORMS of Pokemon. With Vivillon's form also in mind, it took 428 pages to include all the Pokemon and the remaining pages were used for other purposes (check pic). This makes ~60% of the book being occupied by the Pokedex.
If we take the average percentage of the books dedicated to the Pokedex, 62.5%, we can use that to determine the amount of Pokemon forms in the Galar region. This also assumes that each page contains 2 forms of Pokemon as well. The Galar regional Pokedex book has 480 pages. If there are items and a move list kinda stuff in the Pokedex book, we could use the percentage as our estimate, leaving us with ~300 pages of Pokedex. With this in mind, there should be ~600 different forms of Pokemon in the SwSh.
I also have a feeling that Alcremie and the G-max forms will take up a slot or even their own page. So, let's say theres about 20 G-max forms. This would leave the total Pokemon amount to be ~579. Also, the leaks suggests that theres about 74 NEW Pokemon. This means that only ~505 Pokemon from the original 807 Pokemon made it in. However, I didn't count the regional forms so take this number with a grain of salt.