Feature request: Bot / service account support for API integrations

We're integrating Fizzy into our development workflow using the [fizzy-mcp](https://github.com/Fabric-Pro/fizzy-mcp) server to let AI agents interact with boards programmatically. Currently, API access requires Personal Access Tokens tied to human user accounts.

This means we have to create a regular human user to represent a bot — which works, but has drawbacks:
- The "user" consumes a seat and appears in user lists alongside real humans
- No way to distinguish bot actions from human actions in the UI
- No bot-specific permissions or rate limits

## Proposal

Support a **bot / service account** user type that:
- Can generate Personal Access Tokens like regular users
- Is visually distinguishable in the UI (e.g., a bot badge on comments/actions)
- Doesn't consume a regular user seat
- Can be scoped to specific boards or permissions

## Context

Basecamp 3 had [chatbot support](https://github.com/basecamp/bc3-api/blob/master/sections/chatbots.md). A similar concept for Fizzy's API would make it much easier to build integrations where actions are correctly attributed to bots rather than phantom human accounts.

On a related note — we're also looking forward to the official MCP server landing via [#2298](https://github.com/basecamp/fizzy/pull/2298), which would make integrations like this even smoother.

The issue names no Fizzy files or tests; start by reviewing the existing Personal Access Token and user-account behavior, then read the related MCP server proposal in #2298 and Basecamp's chatbot reference. Done would require an agreed design and implementation for bot identity, seat usage, UI attribution, and scoped permissions.

Written by the indexing model from the issue text.