dm: update DM quick start using TiUP Playground (#19637)

[ti-chi-bot]

This is an automated cherry-pick of #19637

What is changed, added or deleted? (Required)

This PR updates the TiDB Data Migration Quick Start guide. Changes include:

• Replacing binary-based deployment instructions with TiUP Playground to simplify setup.
• Adding detailed steps for preparing source databases on Docker, macOS, CentOS, and Ubuntu.
• Simplifying and clarifying the steps for DM configuration and task creation.
• Adding explicit cleanup instructions and actionable examples to improve usability.

These changes aim to make the guide more accurate, complete, and easier to follow for users setting up a local data migration environment.

Which TiDB version(s) do your changes apply to? (Required)

Tips for choosing the affected version(s):

By default, CHOOSE MASTER ONLY so your changes will be applied to the next TiDB major or minor releases. If your PR involves a product feature behavior change or a compatibility change, CHOOSE THE AFFECTED RELEASE BRANCH(ES) AND MASTER.

For details, see tips for choosing the affected versions.

• master (the latest development version)
• v9.0 (TiDB 9.0 versions)
• v8.5 (TiDB 8.5 versions)
• v8.4 (TiDB 8.4 versions)
• v8.3 (TiDB 8.3 versions)
• v8.1 (TiDB 8.1 versions)
• v7.5 (TiDB 7.5 versions)
• v7.1 (TiDB 7.1 versions)
• v6.5 (TiDB 6.5 versions)
• v6.1 (TiDB 6.1 versions)
• v5.4 (TiDB 5.4 versions)

What is the related PR or file link(s)?

• This PR replaces the existing TiDB Data Migration 快速上手指南
• This PR is translated from: dm: update DM quick start using TiUP Playground docs#19925
• Other reference link(s): None

Do your changes match any of the following descriptions?

• Delete files
• Change aliases
• Need modification after applied to another branch
• Might cause conflicts after applied to another branch

[lilin90]

/approve

[ti-chi-bot]

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This pull-request has been approved by: lilin90

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