Remove transition delay for better perceived performance

What does this MR do and why?

Revert "Add animation to the sidebar flyout menu" to improve their perceived performance.

This reverts commit ed9af130.

We decided to keep the transition, but remove its delay. See discussion below.

References

See discussion in #580616 (comment 2886501188)

How to set up and validate locally

This change is only noticable in the "New UI".

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.