Did you export those files using the VS Code extension? The extension uses its export settings to determine where it will look for local copies. For example, if you have the AXIS folder open in VS Code you would need the following export settings to reflect the existing folder structure that you have: objectscript.export.folder setting equal to "", objectscript.export.atelier setting set to true, and objectscript.export.addCategory setting set to false.

I believe this is the same problem described here. You need to add the --check-caps false command to the iris container in your docker-compose.yml file, like this:

...
iris:
    command: --check-caps false
    init: true
...

The SAM 1.1 distribution should have this done for you but that change must not have made it in. I think you can still enter the SAM 2.0 EAP if you'd like to start with the upcoming version.

@Michael Davidovich 
If you have a local folder open there should be two tree views within the ObjectScript view container (the left pane that is shown after clicking the InterSystems logo in the activity bar on the far left). The bottom one is the Projects Explorer and it's only used to create/modify/export server-side project contents (also known as Studio Projects). The top tree (with the Explorer name) is the ObjectScript Explorer where you can Compile/Export/Delete packages and files. Since you don't use server-side source control and need files in your local file system, you can safely ignore the Projects Explorer since they won't be useful for your workflow. Here's a screenshot of what this looks like for me in a locla folder called "langauge-server":

EDIT: If the ObjectScript Explorer isn't showing, make sure you don't have the setting "objectscript.showExpolorer" set to false.

@Michael Davidovich 
You can export individual packages or files from the ObjectScript Explorer. Simply right-click on the node(s) that you want to export and click the "Export" menu option. The command may be better in your use case though because once you have your settings configured properly, you don't need to do anything else besides run the command to update your local copies.

Unfortunately there isn't a way to automatically update your copy if changes are detected. If you make an edit and then try to save it to the server the extension will check if there's a conflict and help you resolve it. If you are working client-side then I wouldn't expect a server conflict though because your local copies (synced with source control of course) should be the "source of truth". You can always re-run the export command before you edit if you want to avoid conflicts.

As for the disappearing disp class, editing the impl class will not force the disp class to be regenerated so its state shouldn't change. That may be due to your Studio configuration being set to hide generated files.

@Michael Davidovich

As a first step I suggest you read through our online documentation to familiarize yourself with common workflows. The extension supports a client-side workflow where you export files to the currently open local folder and handle the source control yourself. To edit client-side, you can use the ObjectScript Explorer to export files. You can also use the Export Code From Server command, which uses the objectscript.export configuration settings to determine what to export. Our extension does not support VS Code's "Download" menu option.

Since the disp class is generated from the spec class you probably don't want to store it in source control but if you still want to export it, you can have the Explorer show generated files before you export a package or if you're using the command you can set the objectscript.export.generatedto true.