By default I use Google and it shows search suggestions, but when I add a custom search engine like https://www.google.com/search?q=, or a completely different one, I don’t get any. I don’t really care where the suggestions are coming from, they could be the same as the one for the default engine.
I did this the hard way by creating my own plugin and then got schooled in the comments on how to actually do it for any bookmark. Link:
https://lemmy.ml/post/1472541?scrollToComments=true
PS: Don’t duplicate your post on a bunch of different servers, it just creates a lot of unnecessary spam for people. I can see at least 3 in a row from lemmy.ml.