brave-browser: Edit person setting is missing

Description

Edit person setting is missing. Found while verifying #4333

Steps to Reproduce

1. Install beta/dev/nightly profile
2. Person settings is missing
3. Can’t edit the the profile to add some cool new profile icons

Actual result:

Expected result:

Reproduces how often:

Easy

Brave version (brave://version info)

Brave	0.65.107 Chromium: 75.0.3770.38 (Official Build) beta(64-bit)
Revision	3860105745f2b12537da9e9f048f14c3f52ba970-refs/branch-heads/3770@{#618}
OS	Linux

Brave	0.66.76 Chromium: 75.0.3770.38 (Official Build) dev(64-bit)
Revision	3860105745f2b12537da9e9f048f14c3f52ba970-refs/branch-heads/3770@{#618}
OS	Linux

Brave	0.67.62 Chromium: 75.0.3770.38 (Official Build)nightly (64-bit)
Revision	3860105745f2b12537da9e9f048f14c3f52ba970-refs/branch-heads/3770@{#618}
OS	Linux

Version/Channel Information:

• Can you reproduce this issue with the current release? No
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the dev channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? N/A
• Does the issue resolve itself when disabling Brave Rewards? N/A
• Is the issue reproducible on the latest version of Chrome? No Chrome still has the option under Chrome name and picture on Chrome release and Beta as well

Miscellaneous Information:

cc: @bsclifton @petemill @rebron @brave/legacy_qa