Now if I type "h my-search" into the omnibar, it goes to google.com/search?q=site%3Anews.ycombinator.com+my-search which gives me only Google search results from HN.
This is using google's algorithm (not the search bar built into whichever website like DDG) which is still the best, especially if you constrain it to one domain name. I also don't have to type the "!"
The prefix messes up google's text prediction. I guess no one from the chromium team is using this feature, since it would be trivial to fix.