Hello,
Sounds like you are accidentally searching for the link in a search engine instead of typing it directly into the web address bar. Open the browser on your phone or PC and tap the very top bar where websites go like bing.com. Clear whatever is in there and type aka.ms/remoteconnect exactly like that. Hit Enter to go straight to the site.
That takes you right to the official page where you can punch in the code shown on your Nintendo Switch 2 screen to get logged in. Give that a shot and see if it works for you.