Reland "Bookmarks: Migrate bookmarks-app to Lit"

Adding the Lit dep broke the build due to new eslint checks.

See PS3 -> PS4 diff for fix.

Original change's description:
> Bookmarks: Migrate bookmarks-app to Lit
>
> This is the last custom element to migrate. As part of the migration:
> - Merging MouseFocusMixin into BookmarksApp, since this is the only
>   client.
> - Removing now unused StoreClientMixin and shared_style.css (Polymer
>   mixin and shared style).
> - Updating store test to test the Lit version of them mixin, which is
>   now used by all bookmarks elements.
>
> Bug: 40943652
> Change-Id: I10b59eebe7612bd7a23187f3c26f1669730f0dac
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6320601
> Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
> Commit-Queue: Rebekah Potter <rbpotter@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1428489}

Bug: 40943652
Change-Id: I5937ba8ee0df323c6651d6450a48b5a38a646ca1
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6329846
Commit-Queue: Rebekah Potter <rbpotter@chromium.org>
Commit-Queue: Demetrios Papadopoulos <dpapad@chromium.org>
Auto-Submit: Rebekah Potter <rbpotter@chromium.org>
Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1428555}
15 files changed
tree: bb783ac4ef31b1a519e4376e06beb5357fcae107
  1. android_webview/
  2. apps/
  3. ash/
  4. base/
  5. build/
  6. build_overrides/
  7. buildtools/
  8. cc/
  9. chrome/
  10. chromecast/
  11. chromeos/
  12. codelabs/
  13. components/
  14. content/
  15. crypto/
  16. dbus/
  17. device/
  18. docs/
  19. extensions/
  20. fuchsia_web/
  21. gin/
  22. google_apis/
  23. gpu/
  24. headless/
  25. infra/
  26. ios/
  27. ipc/
  28. media/
  29. mojo/
  30. native_client_sdk/
  31. net/
  32. pdf/
  33. ppapi/
  34. printing/
  35. remoting/
  36. rlz/
  37. sandbox/
  38. services/
  39. skia/
  40. sql/
  41. storage/
  42. styleguide/
  43. testing/
  44. third_party/
  45. tools/
  46. ui/
  47. url/
  48. webkit/
  49. .clang-format
  50. .clang-tidy
  51. .clangd
  52. .git-blame-ignore-revs
  53. .gitallowed
  54. .gitattributes
  55. .gitignore
  56. .gitmodules
  57. .gn
  58. .mailmap
  59. .rustfmt.toml
  60. .vpython3
  61. .yapfignore
  62. ATL_OWNERS
  63. AUTHORS
  64. BUILD.gn
  65. CODE_OF_CONDUCT.md
  66. codereview.settings
  67. CPPLINT.cfg
  68. CRYPTO_OWNERS
  69. DEPS
  70. DIR_METADATA
  71. LICENSE
  72. LICENSE.chromium_os
  73. OWNERS
  74. PRESUBMIT.py
  75. PRESUBMIT_test.py
  76. PRESUBMIT_test_mocks.py
  77. README.md
  78. WATCHLISTS
README.md

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