refactor: move logic out of main into command handlers to simplify

[wolfeidau]

Moved API client initialization from main.go into individual command handlers (http.go and stdio.go), this enables better seperation of concerns and http specific features.

Example logs from the new HTTP middleware are as follows:

{"level":"info","version":"dev","time":"2026-01-09T16:59:49+11:00","message":"Starting Buildkite MCP server"}
{"level":"info","enabled_toolsets":["all"],"read_only":false,"tool_count":28,"required_scopes":["read_artifacts","read_build_logs","read_builds","read_clusters","read_organizations","read_pipelines","read_suites","read_user","write_builds","write_pipelines"],"time":"2026-01-09T16:59:49+11:00","message":"Registered tools from toolsets"}
{"level":"info","address":"127.0.0.1:3333","time":"2026-01-09T16:59:49+11:00","message":"starting HTTP server"}
{"level":"info","method":"POST","path":"/mcp","status":200,"duration_ms":2177.004167,"client_ip":"127.0.0.1:60001","user_agent":"curl/8.7.1","time":"2026-01-09T16:59:58+11:00","message":"HTTP request"}