Automatic routing does not consider root path or mount location

[nmearl]

Expected Behavior

When embedding a Solara application in a pre-existing Starlette application, automatic routing should consider the root-path command line argument, and generate paths based on the mounted location.

Current Behavior

Automatically generated paths in the Solara app will lead to the root of the Starlette application, where the Solara app is not mounted.

Steps to Reproduce the Problem

1. Create a Starlette application as defined in the Embedding in an Existing Starlette Application page.
2. Mount an existing multi-page Solara app as described in the documentation page.
3. Run the uvicorn server as described, optionally adding SOLARA_ROOT_PATH="/solara" and/or SOLARA_BASE_URL="http://localhost:8865/solara/".
4. Navigate to the mounted location of the Solara app (e.g. http://localhost:8865/solara).
5. Observe that generated links in the Solara app are located at http://localhost/page1 and not http://localhost/solara/page1.

An example application utilizing the multi-page demo is available here: https://github.com/nmearl/solara-test

Specifications

• Solara Version: 1.41.0
• Platform: macOS 15.1.1
• Affected Python Versions: 3.13.0