Automatically clean up user guide & other docs

## Overview

Some documentation is out of date or poorly structured — most notably around API modernisation. Rather than updating it piecemeal, **the goal is to express a clear set of quality criteria to Copilot (e.g. in VS Code) so it can do a full sweep and generate a git patch**.

## Quality Criteria & Known Violations

**Show only current, recommended usage patterns**
→ Text and coding examples use outdated API styles (e.g. `launch_fluent` invocation)

**Keep examples concise — users shouldn't wade through code to grasp a simple idea**
→ Some examples show fully expanded allowed-values output where this adds no value

**Stay on topic — don't explain unrelated features on a given page**
→ Solver settings allowed values are emphasised in the session management page

**Use plain, modern language without being excessively informal**
→ Some sections seem wordier than necessary