I'm fulltime FF but I won't pretend that the in-site (site specific) search works as smoothly as it did (does?) in Chrome
In Chrome you would go to foo.com and you would use their search input and from then on, in your address bar you can type foo (or maybe just f, depending on how often you use foo.com), and press <tab> to search within the site
This is a workflow you get used to
For the longest time I wanted this in FF, but I think the real thing that clicked for me was just heavily leaning on duckduckgo's bangs
(Firefox does have in-site search, which you can use by right clicking in the site's search input and clicking "Add a Keyword for this Search", but I'm not even sure how it works heh)
edit: okay so this is how it works https://support.mozilla.org/en-US/kb/how-search-from-address... and I just added `a` for amazon.com and I typed `a` in the address bar and pressed <enter> and it didn't do anything, hm
edit2: so I guess my main point should have been: Firefox has a manual step for what Chrome did for "free", after you made your first in-site search, which you were probably already going to do