Solidify product variable nomenclature

[jgieringer]

Description

Throughout the product, variable names are used interchangeably and can cause confusion. Examples:

• user == patient == persona == profile (the p_... portion of a conversation p_... folder)
• provider == agent == chatbot (the a_... portion of a conversation p_... folder)
• judge == evaluator (the j_... portion of an evaluation folder)

Fixes

Folder names

• user (u_...)
• chatbot (c_...)
• judge (j_...)
  current conversation: p_claude_opus_4_5_20251101__a_azure_grok_3__t30__r1__20260423_174659/
  proposed conversation: u_claude_opus_4_5_20251101__c_azure_grok_3__t30__r1__20260423_174659/
  judge will be the same j_... with the above dir appended

Conversation filenames

conversation folder:u_claude_opus_4_5_20251101__c_azure_grok_3__t30__r1__20260423_174659/
conversation file: 000a28_Rowan_claude-opus-4-5-20251101_run1.txt
While the folder names contain relevant info, the conversation filenames only store the user model which can be confusing when testing multiple chatbots and looking across different runs' files.

For simplicity, maybe repeat the parent directory without a timestamp?

u_claude_opus_4_5_20251101__c_azure_grok_3__t30__r1__20260423_174659/
  - 000a28_Rowan__u_claude-opus-4-5-20251101__c_azure_grok_3__t30_r1.txt

This might be out of scope but is also so similar, I'm fine with being in same or separate issue.