Upgrade Branch.io system

### What is this about?

- [ ] Consider [the compatible EXPO branch package ](https://github.com/BranchMetrics/react-native-branch-deep-linking-attribution)
- [ ] Ensuring existing features still work
- [ ] Decide if we can remove the submodules

### Scenario

_No response_

### Design

_No response_

### Technical Details

_No response_

### Threat Modeling Framework

_No response_

### Acceptance Criteria

_No response_

### Stakeholder review needed before the work gets merged

- [ ] Engineering (needed in most cases)
- [ ] Design
- [ ] Product
- [ ] QA (automation tests are required to pass before merging PRs but not all changes are covered by automation tests - please review if QA is needed beyond automation tests)
- [ ] Security
- [ ] Legal
- [ ] Marketing
- [ ] Management (please specify)
- [ ] Other (please specify)

### References

_No response_

Start by reviewing the compatible Expo Branch package linked in the issue and the current Branch.io integration. Verify that existing features continue to work and determine whether the submodules can be removed; the issue provides no files or tests to run, and no acceptance criteria define completion.

Written by the indexing model from the issue text.