uv not found from vscode remote terminal

I have defined a `workshop.yaml` with both the `vscode-remote` and `uv` SDKs.

I have connected to the VS Code remote session, but when I open a terminal window, I am unable to run `uv` commands. When I connect to the workshop using `workshop shell`, however, I am able to use `uv` commands.

`workshop.yaml`:

```yaml
name: ...
base: ubuntu@24.04
sdks:
- name: uv
channel: latest/stable
- name: vscode-remote
channel: latest/stable
```

When I compare the `PATH` variable for the `workshop shell` command and the VS Code terminal I see some differences:

`workshop shell`:

```console
/home/workshop/.local/bin:/var/lib/workshop/sdk/uv/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin
```

VS Code terminal:

```console
/home/workshop/.vscode-server/data/User/globalStorage/github.copilot-chat/debugCommand:/home/workshop/.vscode-server/data/User/globalStorage/github.copilot-chat/copilotCli:/home/workshop/.vscode-server/cli/servers/Stable-8b640eef5a6c6089c029249d48efa5c99adf7d51/server/bin/remote-cli:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin
```

Start with the workshop.yaml SDK configuration and compare the environment produced by workshop shell with the VS Code remote terminal. Trace how the vscode-remote SDK initializes the terminal environment and PATH. Done means uv commands work from the connected VS Code terminal as they do from workshop shell, with the behavior covered by an appropriate test if the repository provides one.

Written by the indexing model from the issue text.