[RFC]: Support Claude Tag style of interaction during the inception phase

### Summary

A communication approach in AIDLC to allow remote participants to effectively discuss via instant messaging group (e.g. slack group and channel), then having AI to summarize all discussions in a thread to facilitate the inception phase. Something similar to Claude tag
https://www.anthropic.com/news/introducing-claude-tag

### Motivation

AIDLC workshop brings people together effectively, especially when they are physically sitting in the same room. While I did notice there's natural challenge to support remote participants, especially if they need to have thorough discussions during inception phase. Hence, having a new feature to facilitate discussions among remote participants like Claude Tag do can be a great way to further improve engagements of remote participants.

### Detailed Proposal

Again, similar to claude tag

https://www.anthropic.com/news/introducing-claude-tag

### Alternatives Considered

_No response_

### Drawbacks

_No response_

### Additional Context

_No response_

The issue names no files, tests, or entry points. Start by reviewing the inception-phase workflow and the linked Claude Tag reference, then determine where remote group discussions and thread summaries would fit. Done should be a defined, agreed implementation scope for supporting this interaction pattern.

Written by the indexing model from the issue text.