Fix broken API and process documentation paths

[Copilot]

CI link checker identified missing directories for API reference and processing engine documentation. Links pointed to non-existent paths.

Changes

API reference paths (40 files)

• /influxdb3/{core|enterprise}/api/v3 → /influxdb3/{core|enterprise}/reference/api
• Affected: admin, CLI reference, write-data documentation

Processing engine paths (3 files)

• /influxdb3/{core|enterprise}/process → /influxdb3/{core|enterprise}/get-started/process
• Affected: CLI install documentation

Plugin paths (1 file)

• /influxdb3/{core|enterprise}/process-data/python/plugins/ → /influxdb3/{core|enterprise}/plugins/
• Affected: platform monitoring documentation

Shared templates (20 files)

• Updated /version/api/v3 → /version/reference/api in shared content files
• Updated /version/process/ → /version/get-started/process/ in shared templates

Note: HTTP API endpoint URLs (e.g., /api/v3/query_sql) remain unchanged - these are actual API paths, not documentation links.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Broken links</issue_title>
<issue_description>https://github.com/influxdata/docs-v2/actions/runs/22123928548/job/63949838051#step:12:1</issue_description>

<agent_instructions>Fix broken links and link fragments revealed in these link-checker runs.</agent_instructions>

Comments on the Issue (you are @copilot in this section)

@jstirnaman https://github.com/influxdata/docs-v2/actions/runs/22240567991/job/64342925698?pr=6857

• Fixes Broken links #6831

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[jstirnaman]

Needs to sync up with #6622