[Android] Changed access type for getSearchEngineSourceType

[samartnik]

This fixes crash on debug build

Resolves brave/brave-browser#11022

Submitter Checklist:

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Verified that these changes build without errors on
  • Android
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that these changes pass automated tests (unit, browser, security tests) on
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that all lint errors/warnings are resolved (npm run lint)
• Ran git rebase master (if needed).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Request a security/privacy review as needed.
• Add appropriate QA labels (QA/Yes or QA/No) to include the closed issue in milestone
• Public documentation has been updated as necessary. For instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-compatibility-issues-with-tracking-protection
  • https://github.com/brave/brave-browser/wiki/QA-Guide

Test Plan:

Reviewer Checklist:

• New files have MPL-2.0 license header.
• Request a security/privacy review as needed.
• Adequate test coverage exists to prevent regressions
• Verify test plan is specified in PR before merging to source

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on.
• All relevant documentation has been updated.

[deeppandya]

LGTM

[deeppandya]

@samartnik we need to uplift it to 1.12

[kjozwiak]

Verification PASSED on Samsung S10+ running Android 10 using the following build:

Brave - Nightly 1.14.44 CR: 85.0.4183.69

• ensured that the STR/Cases outlined via [Android] Fix crash on opening search engine in debug build brave-browser#11022 (comment) passed without any issues
• ensured that selecting a SE's via the URL onboarding flow worked without any issues
• ensured that switching SE's via Settings on both normal/PB modes worked without issues
• ensured that switching to DDG via the PB modal worked without issues