Extract expert assistant chat into a single library

Parent issue: #6254

## Description
Extract expert assistant chat into a single library (wishful thinking)

## Tasks
- [ ] Given the MVP and fast moving pace of implementing the feature we are left with two code bases that are doing the same thing
- [ ] Currently we need to keep them in sync and duplicate functionality across repositories
- [ ] Problematic when schemas change, not doing this will double future development time every time, but doing this work early will reduce feature development in half
- [ ] The goal is to have the chat integration as a separate pluggable library that can integrate on both website and flowfuse application
- [ ] The goal is to create a self-contained vue micro-frontend, which can be deployed either via a script tag (in the case of the website) or plugged in the existing FF application frontend
- [ ] The sooner we do this the better, as building ontop will complicate extraction

## Related Issues
- Parent: #6254

Start with parent issue #6254 and compare the two existing expert assistant chat implementations in the website and FlowFuse application frontend. Identify the duplicated functionality and schema dependencies before defining the library boundary; done means both frontends use one self-contained, pluggable chat integration deployable by script tag or within the existing application.

Written by the indexing model from the issue text.