Adds a check whether browser initialised or not inside Intent Handler on Android

[SergeyZhukovsky]

Resolves brave/brave-browser#30773

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Squashed any review feedback or "fixup" commits before merge, so that history is a record of what happened in the repo, not your PR
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally:
  • npm run test -- brave_browser_tests, npm run test -- brave_unit_tests wiki
  • npm run lint, npm run presubmit wiki, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

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, 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-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

It's described in the original issue.

[SergeyZhukovsky]

per @AlexeyBarabash 's suggestion removed query == null as TextUtils.isEmpty checks on null inside

[samartnik]

lgtm

[hffvld]

Verified on Google Pixel 7 using version(s):

Device/OS: Google Pixel 7 [panther_beta-user 14 UPB2.230407.014 release-keys]
Brave build: 1.54.31
Chromium: 114.0.5735.90 (Official Build) canary (64-bit)
Revision: 386bc09e8f4f2e025eddae123f36f6263096ae49-refs/branch-heads/5735@{#1052}

---

STEPS:

1. Close all apps
2. Launch Gmail > Open any email
3. Long tap on any text > Web search
4. Open with Brave Nightly > Verify no crash observed

ACTUAL RESULTS:

• Verified that no crash was observed when opening Brave through Web search option in the apps
• Verified that Brave opened and show the correct info

NOTE: Tried to reproduce it more than 15 times on Nightly with zero repro rate (Still able to repro it with Beta and Prod builds just to compare it)

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