FE default emoji icon persists after clearing status

Summary

The default emoji icon persists next to a username in the notes header. This happens after a user has set their busy status and then removes the status. This was possibly introduced with changes made in !46844 (merged)

Related to #263452 (closed)

Steps to reproduce

Requires the :set_user_availability_status feature flag

From the set status modal

1. Click your user profile in the top right corner
2. From the open dropdown select Edit status (if you have a status set) or Set status
3. Click the busy check box
4. Wait for the success message, then reload the page and open the modal again
5. The busy status should toggled
6. Open the dropdown and click "remove status"
7. Navigate to a merge request you have commented, the speech bubble still appears in the note header

Example Project

What is the current bug behavior?

• The default emoji (speech_bubble) continues to appear next to the user name

What is the expected correct behavior?

• There should be no emoji displayed if there is no message and no custom emoji set

Relevant logs and/or screenshots

No speech bubble - correct	Speech bubble - incorrect

Output of checks

Results of GitLab environment info

Expand for output related to GitLab environment info

(For installations with omnibus-gitlab package run and paste the output of:
`sudo gitlab-rake gitlab:env:info`)

(For installations from source run and paste the output of:
`sudo -u git -H bundle exec rake gitlab:env:info RAILS_ENV=production`)

Results of GitLab application Check

Expand for output related to the GitLab application check

(For installations with omnibus-gitlab package run and paste the output of:
sudo gitlab-rake gitlab:check SANITIZE=true)
(For installations from source run and paste the output of:
sudo -u git -H bundle exec rake gitlab:check RAILS_ENV=production SANITIZE=true)
(we will only investigate if the tests are passing)

Possible fixes