Great! In our case, we need the search page to actually show because we use Algolia and let people do an advanced search from there. I think others, like in the link you showed, prefer a redirection to the home page.
For now, I’m going to see if adding a rewrite_url for that specific link /search/ would work or if I need to create an actual page with that permalink. The latter might be problematic with Soil, tbd!
So my solution to this was to turn off Soil/nice-search and only use the ?s search argument as Polylang redirects an empty search url to a 404 page so it’s impossible to use the search template as is.