docs: add cluster-scoped multi-cluster runtime design

[YangKeao]

What problem does this PR solve?

Issue Number: close #1096

• docs: add cluster-scoped multi-cluster runtime design #1102 <-
• config: add backend cluster schema and multi-port listener config #1103
• backendcluster: add cluster manager and cluster-scoped topology runtime #1104
• metricsreader: move cluster-scoped metrics lifecycle into backend clusters #1105
• router: add port-based routing groups #1106
• backendcluster: route PD and backend traffic through cluster DNS #1107

What is changed and how it works:

Add a design document for TiProxy multi-PD-cluster support.

The document describes:

• the multi-cluster configuration model
• cluster-scoped runtime layout
• dynamic backend-cluster updates through config/API
• port-based routing for multi-port listeners
• cluster-scoped DNS routing requirements
• failure handling and safety expectations

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Notable changes

• Has configuration change
• Has HTTP API interfaces change
• Has tiproxyctl change
• Other user behavior changes

Release note

Please refer to Release Notes Language Style Guide to write a quality release note.

None

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: djshow832

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• OWNERS [djshow832]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-03-23 12:41:29.950094552 +0000 UTC m=+185685.986164812: ☑️ agreed by djshow832.
• 2026-03-23 12:41:44.169992605 +0000 UTC m=+185700.206062866: ✖️🔁 reset by djshow832.
• 2026-03-23 12:42:09.434688165 +0000 UTC m=+185725.470758425: ☑️ agreed by djshow832.