BUG: Some web searches with autocomplete has a delay before working

### Checks

- [x] I have checked that this issue has not already been reported.

- [x] I am using the latest version of Flow Launcher.

- [ ] I am using the prerelease version of Flow Launcher.

### Problem Description

Whenever I use the web search plugin to search on some specific sites such as Youtube I start by typing my action keyword "y" and then type whatever I want to search there's always a small delay where it want to search my default search engine before it snaps into searching on Youtube. I tend to press enter quite fast after I'm done typing so many times it will instead go to Duckduckgo and search for "y linustechtips" or whatever I wanted to search for which is really annoying.
This only applies to some of the search engines though for some unclear reason. Youtube of course has this delay, and also Github, Google Drive and some other I've added, but Google doesn't have it, and Google Maps either.

https://github.com/user-attachments/assets/64c4c389-ced7-43fa-a558-96da4b7aa945

### To Reproduce

1. Open Flow Launch
2. Type the action keyword for Youtube
3. Start typing whatever

### Screenshots

_No response_

### Flow Launcher Version

2.1.3

### Windows Build Number

Version 10.0.19045.3930

### Error Log

```shell

Replace this line with the important log contents.

```

Start by reproducing the delay in Flow Launcher 2.1.3 using the YouTube, GitHub, and Google Drive action keywords, then compare them with Google and Google Maps. Trace the web search plugin and query-selection flow to find why the default search runs first; done means fast entry consistently uses the selected site without sending the query to DuckDuckGo.

Written by the indexing model from the issue text.