Should all category links be placed on the main page?

Question

Search Engine Optimization

Hello! Not so long ago I learned that it’s better to leave only the main links on the main page, but what to do in this case: there are about 350 categories on the site, that if you make a “show all categories” button under the site header, when you click it, a hidden div appears in which all these links to categories would be found (of course, a structured list, not just link spam).
I'll clarify - I'm doing it for the convenience of users, and there are three questions:
1. Is it bad that the main page will have several hundred links (I remind you, the main categories)?
2. How will search engines react to initially hidden links? but they are not hidden from the user - who wants to open them - he will open and go to the right one.
3. Would it be better to load these links via ajax on button click?

Answer 1

Some technology from 10 years ago.
Search engines are much smarter these days.