The F3 menu can be opened from the options menu.

Thank you for your report! 

We're actually already tracking this issue at [MC-300118] The debug overlay can be accessed from all screens - Jira Service Management, so I will resolve and link this ticket as a duplicate. 

I suggest also to browse through the main issue for potential fixes. 

If you would like to add a vote and any extra information to the main ticket it would be appreciated. 

Quick Links: 

📓 Bug Tracker Guidelines – 📧 Mojang Support 

📓 Project Summary – ✍️ Feedback and Suggestions – 📖 Minecraft Wiki