2,600 character limit, with a "see more" cutoff at ~265 chars. Both shown live as you type.
LinkedIn truncates the About section at roughly 265 characters with a "see more" link. Those ~265 chars are everything visitors see by default — they decide whether to expand and read the rest. That makes the opening of your About section the most important block on your entire profile.
If your hook worked and the visitor expanded, the rest of the About should: