Thanks! 

Adding the self-signed certificate to the operating System's root certificates (in my case, the Mac keychain under System) worked.

Once the certificate was added, I didn't need to set http.proxyStrictSSL to false.

I think this is not working anymore. I tried installing the v2.12.6 but got the message that the extension is not available from Visual Studio Code for the Web 🙁

I am having this same problem and I am using the latest extension. 

I added the 

"http.proxyStrictSSL": false

to the User settings.json , which is the same as

But still getting the error: 
 

Check your server details in Settings (vgorillaaws[VGORILLA]).

request to https://ec2-x.x.x.x.us-east-2.compute.amazonaws.com/api/atelier/ failed, reason: self signed certificate

I am using [2.5.0] - 2024-05-02 InterSystems Language Server