[Backport 2.x] Conditionally change where avatar shows up

[opensearch-trigger-bot]

Backport e3da9b4 from #2082.

[codecov]

Codecov Report

Attention: Patch coverage is 37.50000% with 5 lines in your changes missing coverage. Please review.

Project coverage is 71.04%. Comparing base (2b5028b) to head (6ec6eea).
Report is 1 commits behind head on 2.x.

Files	Patch %	Lines
public/apps/account/account-nav-button.tsx	40.00%	0 Missing and 3 partials ⚠️
public/apps/account/account-app.tsx	33.33%	0 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##              2.x    #2088      +/-   ##
==========================================
- Coverage   71.17%   71.04%   -0.13%     
==========================================
  Files          96       96              
  Lines        2598     2604       +6     
  Branches      380      392      +12     
==========================================
+ Hits         1849     1850       +1     
  Misses        649      649              
- Partials      100      105       +5     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.