Logic Pro not connecting to the internet

If Logic Pro itself won’t connect, I’d first check whether the Mac has normal internet access in Safari and whether Apple’s System Status shows any issue with Apple services.

If the problem is only in Logic, the exact symptom matters. Is Logic failing to download the Sound Library, validate your purchase, access something in the Logic Pro app, or are you seeing a specific error message?

I wouldn’t reinstall Logic yet. The exact message would help narrow this down quite a bit.