Reland "[UNOp2][Android] Make account info acquisition as synchronous as possible"

This is a reland of commit d2bae94e74f98733f696afb04cd31e2237d5d17a

Test issues that caused the revert were fixed by
https://crrev.com/c/5563689.

Original change's description:
> [UNOp2][Android] Make account info acquisition as synchronous as possible
>
> ProfileDataCache extensively uses Promise while populating account
> info. Since fulfilled promises still post a task to the UI thread that
> is executed on the next frame - the profile data won't be available
> until those tasks are executed (this was taking up to 3 frames prior to
> this CL). This CL addresses the issue by adding some explicit checks
> for whether the promise is already fulfilled. This is a temporary
> solution that will be simplified after https://crbug.com/341948846 is
> addressed.
>
> Bug: 330357665
> Change-Id: Ie4ce868555e2760fd59ef47755149b80c1c0ff10
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5547669
> Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
> Reviewed-by: Menghan Yang <myuu@google.com>
> Commit-Queue: Boris Sazonov <bsazonov@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1304940}

Bug: 330357665, 342370154
Change-Id: I133200be907a98d0657cd6a2b67704ad0ef081fd
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5569251
Reviewed-by: Menghan Yang <myuu@google.com>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Boris Sazonov <bsazonov@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1305688}
3 files changed
tree: f3b343bb50765cd4cab309cd0f5c50a0859949ee
  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. courgette/
  16. crypto/
  17. dbus/
  18. device/
  19. docs/
  20. extensions/
  21. fuchsia_web/
  22. gin/
  23. google_apis/
  24. google_update/
  25. gpu/
  26. headless/
  27. infra/
  28. ios/
  29. ipc/
  30. media/
  31. mojo/
  32. native_client_sdk/
  33. net/
  34. pdf/
  35. ppapi/
  36. printing/
  37. remoting/
  38. rlz/
  39. sandbox/
  40. services/
  41. skia/
  42. sql/
  43. storage/
  44. styleguide/
  45. testing/
  46. third_party/
  47. tools/
  48. ui/
  49. url/
  50. webkit/
  51. .clang-format
  52. .clang-tidy
  53. .clangd
  54. .eslintrc.js
  55. .git-blame-ignore-revs
  56. .gitallowed
  57. .gitattributes
  58. .gitignore
  59. .gitmodules
  60. .gn
  61. .mailmap
  62. .rustfmt.toml
  63. .vpython3
  64. .yapfignore
  65. ATL_OWNERS
  66. AUTHORS
  67. BUILD.gn
  68. CODE_OF_CONDUCT.md
  69. codereview.settings
  70. CPPLINT.cfg
  71. DEPS
  72. DIR_METADATA
  73. LICENSE
  74. LICENSE.chromium_os
  75. OWNERS
  76. PRESUBMIT.py
  77. PRESUBMIT_test.py
  78. PRESUBMIT_test_mocks.py
  79. README.md
  80. WATCHLISTS
README.md

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