docs: consolidate and archive documentation

- Move 30+ outdated docs to docs/_archive/
- Move obsolete root files to _archive/
- Update README.md (Better Auth, current features)
- Update docs/README.md (new architecture diagram)
- Update docs/quick-reference.md (consolidated)
- Update docs/project-status.md (March 2026 state)
- Update docs/nao6-quick-reference.md (14 actions, Docker services)
- Update docs/implementation-guide.md (Better Auth, git submodule)
- Update docs/proposal.tex (timeline updates)
- Archive errors.txt, plugin_dump.json, test HTML files

docs/proposal.tex

@@ -107,7 +107,7 @@ This work addresses a significant bottleneck in HRI research. By creating HRIStu
 \hline
 September & Finalize and submit this proposal (Due: Sept. 20).
 
-Submit IRB application for the user study. \\
+Submit IRB application for the study. \\
 \hline
 Oct -- Nov & Complete final implementation of core HRIStudio features.
 
@@ -119,13 +119,15 @@ Begin recruiting participants. \\
 \hline
 \multicolumn{2}{|l|}{\textbf{Spring 2026: Execution, Analysis, and Writing}} \\
 \hline
-Jan -- Feb & Upon receiving IRB approval, conduct all user study sessions. \\
+Jan -- Feb & Run pilot tests with platform.
+
+Refine based on testing feedback. \\
 \hline
-March & Analyze all data from the user study.
+March & Execute user study sessions (10-12 participants).
 
-Draft Results and Discussion sections.
+Analyze data from the user study.
 
-Submit ``Intent to Defend'' form (Due: March 1). \\
+Draft Results and Discussion sections. \\
 \hline
 April & Submit completed thesis draft to the defense committee (Due: April 1).