In case anyone is still having this issue here are some steps to take that will solve this for you.
A couple of things to keep in mind your droplets have to be in the same region as the managed DB to use the private connection.
Now, if that’s all set here’s the next steps. This makes the assumption that you are adding private networking after already having created your managed db.
Step 1 - If you’ve enabled Private Networking for your droplet and followed the instructions to add the private IP address you can SSH into your droplet and use the Connection String with Flags to make sure you’re managed DB knows to let your droplet traffic through.
Step 2(A) - It worked? Great! Your app is probably not configured correctly to use the private connection.
Step 2(B) - The connection is still timing out? No worries, copy the private IP address of the droplet and then navigate to your managed DB settings, then add the private IP address as under “Trusted sources”, make sure you specifically use the IP address, and then save.
Step 2© - Test your connection using Connection String > Flags again from your droplets ssh session. You should now be connecting!
For some reason, it appears that using the tags does not add the private IP to the managed DB’s trusted sources list, but adding it manually works. This isn’t very scalable though 🤔😡