fix: restore shared prop forwarding across components

[dawoodkhan82]

Description

Follow-up to #13644 and #13623. This restores shared props that stopped reaching their component implementations after frontend prop partitioning:

• forwards Column props so panel and compact variants apply
• restores Dataset root, HTML padding, JSON/Plot theme_mode, Tab scale, and Textbox validation-error behavior
• injects the resolved theme_mode into the shared app config for all consumers
• corrects the shared padding contract to boolean
• adds focused Dataset/Textbox unit coverage and a live-app Playwright test covering every affected component

This PR is temporarily stacked on recovery PR #13679. After #13679 restores the pre-push main tree, this PR should be retargeted to main.

Related: #13623

AI Disclosure

• I used AI to audit shared-prop consumers, implement the fixes and tests, and draft this description. Every changed line was self-reviewed.
• I did not use AI

🎯 PRs Should Target Issues

This is the reviewed follow-up for #13623 after #13644 was accidentally marked merged by a misdirected direct push.

Testing and Formatting Your Code

• CI=1 pnpm exec vitest run --config .config/vitest.config.ts js/column/Column.test.ts js/dataset/Dataset.test.ts js/html/HTML.test.ts js/json/JSON.test.ts js/plot/Plot.test.ts js/tabitem/TabItem.test.ts js/textbox/Textbox.test.ts — 158 passed, 7 todo
• pnpm exec playwright test js/spa/test/shared_props.spec.ts --config=.config/playwright.config.js — 1 passed
• pnpm build — passed
• Prettier — passed for changed frontend files
• Ruff format/check — passed for the demo
• Repository-wide pnpm ts:check still reports 16 unrelated baseline/environment errors; the shared HTML padding diagnostic from this change was resolved.

[gradio-pr-bot]

🪼 branch checks and previews

•	Name	Status	URL
	Spaces	ready!	Spaces preview
	Website	ready!	Website preview
	Storybook	ready!	Storybook preview

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Install Gradio from this PR

pip install https://huggingface.co/buckets/gradio/pypi-previews/resolve/986430ee9e1b61ea427bc83abe224d6fa22719af/gradio-6.20.0-py3-none-any.whl

Install Gradio Python Client from this PR

pip install "gradio-client @ git+https://github.com/gradio-app/gradio@986430ee9e1b61ea427bc83abe224d6fa22719af#subdirectory=client/python"

Import Gradio JS Client from this PR via CDN

import { Client } from "https://huggingface.co/buckets/gradio/npm-previews/resolve/986430ee9e1b61ea427bc83abe224d6fa22719af/browser.js";