According to the azure app service sidecar documentation, the default value for the inheritAppSettingsAndConnectionStrings sidecar setting is true, so when unset, it the sidecar should inherit the main environment variables. This is the case when using ARM templates, the Azure CLI and the like.
However, when the box is unchecked in the portal, it is set to false, which results in the sidecar * not * inheriting the environment variables. If you make any updates to the sidecar in the portal, the default then becomes inheritAppSettingsAndConnectionStrings=false, but if you update it with the CLI the inheritAppSettingsAndConnectionStrings=undefined which defaults to true.
This effectively means that the portal and automation tools have the opposite defaults * and * that the difference is indistinguishable in the portal (since both undefined and false result in an un-checked checkbox) ! Hence you may have no way of knowing the difference between the two un-checked behaviors, -- and even worse, unrelated changes to the app service in the portal may update the default value from undefined to false.
So in short, good luck to you, and don't trust the inheritAppSettingsAndConnectionStrings setting, so you may want to set environment variables for the sidecar right there in the sidecar settings (which you can do).