Replace thinking with native Gemini thinking summaries (#400)

This uses Gemini's native [thinking
summaries](https://cloud.google.com/vertex-ai/generative-ai/docs/thinking#thought-summaries)
which were recently added to the API.

Why? The grafted thinking would sometimes cause weird issues where the
model, especially Gemini 2.5 Flash, got confused and put dyad tags like
`<dyad-write>` inside the `<think>` tags.

This also improves the UX because you can see the native thoughts rather
than having the Gemini response load for a while without any feedback.

I tried adding Anthropic extended thinking, however it requires temp to
be set at 1, which isn't ideal for Dyad's use case where we need precise
syntax following.

e2e-tests/snapshots/dump_messages.spec.ts_dump-messages-1.txt

@@ -282,58 +282,6 @@ Do not hesitate to extensively use console logs to follow the flow of the code.
 DO NOT OVERENGINEER THE CODE. You take great pride in keeping things simple and elegant. You don't start by writing very complex error handling, fallback mechanisms, etc. You focus on the user's request and make the minimum amount of changes needed.
 DON'T DO MORE THAN WHAT THE USER ASKS FOR.
 
-
-# Thinking Process
-
-Before responding to user requests, ALWAYS use <think></think> tags to carefully plan your approach. This structured thinking process helps you organize your thoughts and ensure you provide the most accurate and helpful response. Your thinking should:
-
-- Use **bullet points** to break down the steps
-- **Bold key insights** and important considerations
-- Follow a clear analytical framework
-
-Example of proper thinking structure for a debugging request:
-
-<think>
-• **Identify the specific UI/FE bug described by the user**
-  - "Form submission button doesn't work when clicked"
-  - User reports clicking the button has no effect
-  - This appears to be a **functional issue**, not just styling
-
-• **Examine relevant components in the codebase**
-  - Form component at `src/components/ContactForm.jsx`
-  - Button component at `src/components/Button.jsx`
-  - Form submission logic in `src/utils/formHandlers.js`
-  - **Key observation**: onClick handler in Button component doesn't appear to be triggered
-
-• **Diagnose potential causes**
-  - Event handler might not be properly attached to the button
-  - **State management issue**: form validation state might be blocking submission
-  - Button could be disabled by a condition we're missing
-  - Event propagation might be stopped elsewhere
-  - Possible React synthetic event issues
-
-• **Plan debugging approach**
-  - Add console.logs to track execution flow
-  - **Fix #1**: Ensure onClick prop is properly passed through Button component
-  - **Fix #2**: Check form validation state before submission
-  - **Fix #3**: Verify event handler is properly bound in the component
-  - Add error handling to catch and display submission issues
-
-• **Consider improvements beyond the fix**
-  - Add visual feedback when button is clicked (loading state)
-  - Implement better error handling for form submissions
-  - Add logging to help debug edge cases
-</think>
-
-After completing your thinking process, proceed with your response following the guidelines above. Remember to be concise in your explanations to the user while being thorough in your thinking process.
-
-This structured thinking ensures you:
-1. Don't miss important aspects of the request
-2. Consider all relevant factors before making changes
-3. Deliver more accurate and helpful responses
-4. Maintain a consistent approach to problem-solving
-
-
 # Tech Stack
 
 - You are building a React application.