This is super interesting, so much so that I spent a little while trying to test an idea, and it worked.
It's not done with Vivaldi itself, though. As far as I can see, there is currently no way to do it with Vivaldi's features specifically. And your feature request might never be answered if too few people vote on it.
So, if you're interested in a hacky solution, I've got one for you: an HTML file with some Javascript. I'm not entirely sure if it will work in a non-Linux system, I can't see why not.
For this, we need the file. It's extremely simple code:
<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=100, initial-scale=1.0"> <title>Testing Web Search</title> </head> <body> <h1>Hello World!</h1> <p>You have to manually close the tab. :'(</p> <script> var url = new URL(window.location); var sp = url.searchParams.get("q"); var urls = [ "https://www.google.com/search?q=", "https://www.duckduckgo.com/?q=", "https://www.bing.com/search?q=" ]; var interval = setInterval(function() { var url = urls.pop(); if(!!url) { window.open(url + sp, "_blank"); } else { clearInterval(interval); } }, 100); </script> </body> </html>You need to edit the URLs, to any you wish to use. Make sure the place where %s would go is the last and don't put it there on the list. (I just wanted to keep it simple, so no fancy replacements. Put all non-term parameters before the %s parameter would go.)
(If you don't know how to add URLs to the file, let me know and I'll write them for you.)
Save the file somewhere in your home/user directory as mymanywebsearch.html (for example, anything that ends with .html).
Now go to Vivaldi > Settings > Search and add a new search engine. Instead of a web URL, you'd point it to the file as such: file://[path]/subdir/mymanywebsearch.html?q=%s
(The path depends on your system. For example, in Linux it is: file:///home/tyrion/scripts/mymanywebsearch.html?q=%s and for Windows I think it would be file:///C:/Windows/Users/tyrion/scripts/mymanywebsearch.html?q=%s)
On the search engine you can create your desired nickname. You mentioned s, so you can use that.
Next, permissions. I couldn't manually insert a new rule in Vivaldi > Settings > Privacy and Security > Website permissions. It glitches out for the local file, HOWEVER, the permissions can be set when accessing the file (below is how).
So, now you can try typing in the address bar s term (where s is your search engine nickname and term is whatever you want to search).
Nothing will happen if you have Global permissions set to block all pop ups! That's okay! The browser is doing its job by blocking stuff that's popping up on its own.
On the right corner of the address field, you will see a small icon with a square outline and a small red symbol.
d0642b6a-8598-405d-9e72-bb9fee7818bc-image.png
Hovering over it, you'll get the tooltip: "Blocked Popup Pages". Click on it, and a small dialog will show with the URLs blocked, and the checkboxes "Block Popups" (checked) and "Always Allow" (unchecked). Check "Always Allow". Then you can refresh the "page" and the tabs should start opening.
Unfortunately, I couldn't find a way to close that tab, so you'll always have to manually close it.
I know it's not what you were asking for, but I got really curious if this could be achieved and so I wanted to share it.
