Revert the disabling of WebSQL after finding extension breakage

[bsclifton]

Speed dial extension was affected; may impact others too.

Fixes brave/brave-browser#8542
Unfixes brave/brave-browser#7522

---

Revert "Merge pull request #4463 from brave/disable_websql"

This reverts commit a50fa1d, reversing
changes made to cd4edd3.

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-Protection-Mode
  • 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:

See brave/brave-browser#8542

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.

[bsclifton]

Needs uplift to 1.6 after we test on Nightly. Queueing new Nightly now...

[kjozwiak]

Verification PASSED on macOS 10.15.3 x64 using the following build

Brave | 1.7.44 Chromium: 80.0.3987.132 (Official Build) nightly (64-bit)
-- | --
Revision | fcea73228632975e052eb90fcf6cd1752d3b42b4-refs/branch-heads/3987@{#974}
OS | macOS Version 10.15.3 (Build 19D76)

• Went through the STR outlined under certain extensions breaking due to WebSQL being disabled brave-browser#8542 (comment) and ensured that the extension can be installed without any issues
• Clicked around and ensured that the extension actually works as expected