bridge: adopt "Gateway bridge" terminology (phase 1)

[benvinegar]

Summary

• rename user-facing "Slack bridge" wording to "Gateway bridge" across docs, skills, and operator/runtime messaging
• update bridge startup/log copy in both runtimes (bridge.mjs, broker-bridge.mjs)
• keep compatibility-sensitive technical identifiers unchanged (slack-bridge/ paths, SLACK_* env vars, existing artifact names)

Scope / non-goals

This is phase 1 (terminology-only).

No behavior changes, no path renames, no env var renames.

Validation

• npm run lint
• npm test

(One pre-existing Biome warning remains in slack-bridge/broker-bridge.mjs for an unused catch variable.)

[greptile-apps]

Greptile Summary

This PR successfully renames user-facing "Slack bridge" terminology to "Gateway bridge" across 21 files including documentation, scripts, agent skills, and runtime code. The changes are consistent and well-executed:

• Scope: Updated comments, log messages, documentation, and user-facing strings
• Technical identifiers preserved: Directory name (slack-bridge/), environment variables (SLACK_*), and file paths remain unchanged as intended for phase 1
• Completeness: All user-facing references have been updated, with no remaining "Slack bridge" terminology found in the codebase
• No functional changes: This is purely a terminology update with no behavior modifications

The renaming provides clearer abstraction for the bridge component's role as a gateway between Slack and the agent system.

Confidence Score: 5/5

• This PR is safe to merge with no risk
• This is a pure terminology change with zero functional impact. All 21 files consistently update user-facing strings, comments, and documentation from "Slack bridge" to "Gateway bridge" while preserving technical identifiers as intended. The author validated with lint and tests, and the changes are straightforward string replacements with no logic modifications.
• No files require special attention

Important Files Changed

Filename	Overview
slack-bridge/bridge.mjs	Updated user-facing log message to use "Gateway bridge" terminology
slack-bridge/broker-bridge.mjs	Updated header comment and startup log message to use "Gateway bridge" terminology
pi/skills/control-agent/SKILL.md	Updated all references from "Slack bridge" to "Gateway bridge" throughout agent documentation
pi/skills/control-agent/startup-pi.sh	Updated script header, comments, and echo messages to use "Gateway bridge" terminology
AGENTS.md	Updated architecture diagram and agent boot phase table to use "Gateway bridge" terminology with clarifying note about slack-bridge directory
bin/doctor.sh	Updated health check messages and warnings to use "gateway bridge" terminology

_{Last reviewed commit: 2807686}