Twine doesn't set any hard limit on how big a single story can be, whether on number of passages, amount of text, or number of links.
If you're using browser Twine, you are limited by the amount of storage space your browser allows Twine. You can see the amount of space available as a percentage in the corner of the Story Library screen.
If you're using app Twine, you're limited by the amount of space on your computer, but you're very unlikely to be limited by this in practice.
However, you may notice Twine slowing down while editing a large story. Exactly when this becomes evident depends on many things: how powerful your computer is, how large the Twine window onscreen is (drawing more of the Story Map screen at one time takes more resources, of course), how you've arranged your story, and more. As a result, it's hard to advise specific actions if you notice that Twine is sluggish with your story.
One possibility, though, is to split your story into multiple stories.