[Desktop] sync button in profile manager

[LaurenWags]

Description

In 1.14.x and 1.15.x (so far), there are multiple issues with the profile manager. First one is:

1. There is a large "Turn on sync" button which should be removed (if you click on it, this causes perf issues, browser freezing, so we should remove the button or address these issues)

Second one was moved to #11444

Steps to Reproduce

1. Clean profile with 1.14.x or 1.15.x
2. Create a second profile
3. Click on one of the profile icons --> See large "Turn on sync" button

Actual result:

Step 3:

Expected result:

No sync button on profile manager:

Reproduces how often:

easily

Brave version (brave://version info)

1.14.63 (Dev)
1.15.6 (Nightly)

Version/Channel Information:

• Can you reproduce this issue with the current release? 1.12.x C84 no, 1.13.x CR 85.0.4183.69 not atm, but it is currently behind the others in CR version
• Can you reproduce this issue with the beta channel? yes, 1.14.63 CR 85.0.4183.78
• Can you reproduce this issue with the nightly channel? yes 1.15.6 CR 85.0.4183.78

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields?
• Does the issue resolve itself when disabling Brave Rewards?
• Is the issue reproducible on the latest version of Chrome?

Miscellaneous Information:

cc @rebron @mkarolin @Brave-Matt

[LaurenWags]

Verified passed with

Brave | 1.14.74 Chromium: 85.0.4183.83 (Official Build) dev (64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | macOS Version 10.14.6 (Build 18G3020)

• Verified STR from description

---

Verification passed on

Brave | 1.14.74 Chromium: 85.0.4183.83 (Official Build) dev (64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | Windows 10 OS Version 1903 (Build 18362.1016)

• Verified STR from description

Profile 2:

Profile 1:

---

Verification passed on

Brave	1.14.75 Chromium: 85.0.4183.83 (Official Build) dev (64-bit)
Revision	94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS	Ubuntu 18.04 LTS