Fix race condition of `menu-expanded` and top nav

What does this MR do?

This MR fixes a race condition where the responsive menu redesign and the state of the top nav bar can become out of sync if the user starts clicking "Menu" right away.

Screenshots (strongly suggested)

How to test?

You'll need to enable the :combined_menu feature flag locally.

Before (on master)	After (this MR)
20210609_before_race_condition	20210609_fix_race_condition

You'll notice in the Before, the top nav bar becomes out of sync with the menu's visibility. This is fixed now 🎉

Does this MR meet the acceptance criteria?

Conformity

• [ ] I have included a changelog entry, or it's not needed. (Does this MR need a changelog?) Not needed since it's behind a feature flag.
• I have added/updated documentation, or it's not needed. (Is documentation required?)
• I have properly separated EE content from FOSS, or this MR is FOSS only. (Where should EE code go?)
• I have added information for database reviewers in the MR description, or it's not needed. (Does this MR have database related changes?)
• I have self-reviewed this MR per code review guidelines.
• This MR does not harm performance, or I have asked a reviewer to help assess the performance impact. (Merge request performance guidelines)
• I have followed the style guides.
• This change is backwards compatible across updates, or this does not apply.

Availability and Testing

• I have added/updated tests following the Testing Guide, or it's not needed. (Consider all test levels. See the Test Planning Process.)
• I have tested this MR in all supported browsers, or it's not needed.

Related to #301143 (closed)