Laggy search and navigation feedback

I've been using the new Nuxt website for a few months right now and wanted to provide some UX feedback based on my developer usage. For context I find myself using the docs multiple times a day.

1. When searching the docs the text input field gets blocked from rendering which means there is a disconnect with what you're typing and what is displayed. I don't think the search results need to be instant but what you're typing in the text input should not be blocked. For example in the recording below I am constantly typing but it's really choppy and I finished typing a full 10 seconds before my typed text is actually completely displayed.

2. The animations for the menus are cool but the artificial delay trips me up multiple times a day if I'm moving "too fast". I know where I want to go but frequently find myself needing to slow down or try again to get to the menu that I want because of the delay.

All if this feedback is in contrast to the previous website which I didn't have nearly as much friction using when navigation around and didn't feel like I was be throttled when navigating through the docs. If this was only a marketing page that would be fine but since it's also developer documentation I think it should be a bit more responsive.

Start by reproducing the documented search-input lag and menu animation delays in the Nuxt website, using the recordings and interaction details in this issue. Trace the affected search and navigation entry points, then verify that typing remains responsive and menus no longer impose disruptive delays.