Support global user instructions for new rooms

## Problem

Every new room starts without any personal context or instructions.

As a result, users have to repeatedly explain how they prefer to work and how they expect the agent to behave. This includes communication preferences, working principles, expected output quality, and general constraints.

For users who create multiple rooms, this creates unnecessary repetition and leads to inconsistent agent behaviour.

## Proposed feature

Add a global user instruction field that is automatically included in the initial context of every newly created room.

The user should be able to define their preferred way of working and expected agent behaviour once, without having to repeat it in every new conversation.

## Example use cases

A global instruction could contain rules such as:

- Prefer concise but technically precise answers.
- Ask for clarification when requirements are ambiguous instead of making assumptions.
- Think before acting and explain important assumptions or trade-offs.
- Prefer simple solutions over unnecessary complexity.
- Make only minimal and targeted changes.
- Do not perform destructive or external actions without explicit confirmation.
- Validate results before claiming that a task is complete.
- Use Markdown and provide implementation-oriented recommendations where appropriate.
- After completing a task, proactively suggest the most useful next best action, such as a logical follow-up step, validation, improvement, or decision the user may want to make.

This could also support coding-agent guidelines such as commonly shared Karpathy-style rules:

- Think before coding.
- Keep solutions simple.
- Make surgical changes only.
- Define and verify success criteria.
- Recommend a next best action when it would help the user make progress.

## Expected behaviour

- Users can create and edit one global instruction in their settings.
- The instruction is automatically applied to every new room.
- The global instruction is visible when creating a room and from within an existing room.
- Users can disable the global instruction for an individual room if needed.
- Changes to the global instruction affect newly created rooms by default and do not silently change the context of existing rooms.
- The UI makes it clear that the global instruction is active and included in the agent context.
- The agent can use the global instruction to proactively recommend a relevant next best action, without unnecessarily extending every response.

## Why this matters

A persistent global instruction would make the agent more consistent and useful across rooms while reducing repetitive onboarding messages.

Including a “next best action” expectation would make the agent more proactive. Instead of only answering the immediate question, it could identify a relevant follow-up step where appropriate—for example, proposing a validation step after producing code, suggesting a decision after an analysis, or identifying missing information before implementation.

It would be especially valuable for users with established working styles or recurring quality expectations, such as software development, research, documentation, and technical architecture work.

## Acceptance criteria

- [ ] A user can define and edit one global instruction.
- [ ] The global instruction is automatically included in every newly created room.
- [ ] The user can see whether the global instruction is active in a room.
- [ ] The user can disable the global instruction for an individual room.
- [ ] Updating the global instruction does not retroactively modify existing rooms by default.
- [ ] The global instruction supports multi-line text and Markdown formatting.
- [ ] The global instruction can contain agent behaviour rules, including an instruction to suggest a relevant next best action where appropriate.

No files or tests are named. Start by locating the existing settings and room-creation flows, then trace how initial agent context is assembled. Done means the acceptance criteria are met for global instruction editing, new-room application, per-room disabling, visibility, Markdown, and no retroactive changes.

Written by the indexing model from the issue text.