Issue: [FEATURE] Add payment type to Get Intent Response (v2)

### Feature Description

We need to return `payment_type` in `Get Intent`. Required by SDK

### Possible Implementation

Add a field `payment_type` to Get Intent Response

### Have you spent some time checking if this feature request has been raised before?

- [x] I checked and didn't find a similar issue

### Have you read the Contributing Guidelines?

- [x] I have read the [Contributing Guidelines](https://github.com/juspay/hyperswitch/blob/main/docs/CONTRIBUTING.md)

### Are you willing to submit a PR?

Yes, I am willing to submit a PR!

Resolution: <think>
PR Context:
- Title: feat(router): Add payment_type to Get Intent response (v2)
- Merged: 2025-08-28T06:22:39Z
- Files changed: 3 files
- Commits: 3 commits

Implementation approach:
## Type of Change
<!-- Put an `x` in the boxes that apply -->

- [ ] Bugfix
- [ ] New feature
- [x] Enhancement
- [ ] Refactoring
- [ ] Dependency updates
- [ ] Documentation
- [ ] CI/CD

## Description
<!-- Describe your changes in detail -->
- Add `payment_type` to Payments Get Intent response

### Additional Changes

- [x] This PR modifies the API contract
- [ ] This PR modifies the database schema
- [ ] This PR modifies application configuration/environment variables

<!
</think>

To implement this, you'll need to modify:


**Detailed Implementation:**


**Commit 1:** feat(router): Add payment_type to Get Intent response (v2) (#9066)
Co-authored-by: Hrithikesh <61539
Files to modify:


**crates/api_models/src/payments.rs**
  Modify existing code

**crates/router/src/core/payments/transformers.rs**
  Modify existing code