Most likely, leagues cannot be loaded because Cloudflare suspects you are a bot. GGG uses Cloudflare's bot protection services to ensure fair access to the trade site, especially during league launch.
The permanent solution to this is to change the IP address or write to GGG support.
If you are ok with the temporary solution, you will need to complete a CAPTCHA every ~15 minutes.
Click on "Browser" button. Wait untill you see a CAPTCHA and complete it. Alternatively, you can get a lightweight bot check, which means you just wait ~5 seconds and see the screenshot below.
Once you see the barely visible text with the list of leagues, click on the "Retry" button, now everything should work.
If you've opened Browser, waited for a while and see nothing, then the problem is with the network. A simple PC reboot usually helps.
People have encountered some weirdness related to VPN and DNS settings.