refactor: Remove deprecated binlog endpoint (backport #538)

[mergify]

In binlog v2, we have our custom indexer

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This is an automatic backport of pull request #538 done by Mergify.

[greptile-apps]

Greptile Summary

Removes the deprecated search_binary_log server method and its corresponding /database/binary/logs/<log> POST endpoint, replaced by the custom indexer in binlog v2.

• database_server.py: deletes search_binary_log — no remaining callers in the repo.
• web.py: removes the POST route for per-log searching; the GET /database/binary/logs listing endpoint is unchanged.

Confidence Score: 5/5

Pure deletion of a deprecated method and its route — no logic changes, no remaining callers, no side effects on other endpoints.

Both deleted units (the search_binary_log method and its POST route) have no remaining references in the codebase, and the sibling binary_logs listing endpoint is untouched.

No files require special attention.

Important Files Changed

Filename	Overview
agent/database_server.py	Removes the search_binary_log method entirely; no remaining callers, binary_logs property is untouched.
agent/web.py	Removes the /database/binary/logs/<log> POST route; the sibling GET /database/binary/logs listing endpoint is unaffected.

Sequence Diagram

sequenceDiagram
    participant Client
    participant web.py
    participant DatabaseServer

    Note over Client,DatabaseServer: REMOVED (deprecated)
    Client->>web.py: "POST /database/binary/logs/{log}"
    web.py->>DatabaseServer: search_binary_log(log, database, ...)
    DatabaseServer-->>web.py: events[]
    web.py-->>Client: JSON response

    Note over Client,DatabaseServer: RETAINED
    Client->>web.py: GET /database/binary/logs
    web.py->>DatabaseServer: binary_logs (property)
    DatabaseServer-->>web.py: log list
    web.py-->>Client: JSON response

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