[refactor 1/n] Web toolkit

[zechengz]

Description

Clean and refactor the web toolkit. The functionality is not changed.

Part of #1764

Checklist

Go over all the following points, and put an x in all the boxes that apply.

• I have read the CONTRIBUTION guide (required)
• I have linked this PR to an issue using the Development section on the right sidebar or by adding Fixes #issue-number in the PR description (required)
• I have checked if any dependencies need to be added or updated in pyproject.toml and uv lock
• I have updated the tests accordingly (required for a bug fix or a new feature)
• I have updated the documentation if needed:
• I have added examples if this is a new feature

[Wendong-Fan]

thanks @zechengz !