FOSS. It works in Mozilla Firefox 133.0 (64-bit) under Windows 10, but you have to enter everything manually, not visually, without using the keyboard, as is implemented in similar add-ons. Some sites are incompatible with such a search due to the replacement of the space character (%20) with the “+” character.

Upd. The add-on no longer works: "SyntaxError: JSON.parse: unexpected end of data at line 1 column 1 of the JSON data".

Currently broken: "TypeError: NetworkError when attempting to fetch resource.[Learn More]" when adding a new engine.

Does what needs to do pretty well except it doesn't support POST method for search engines like startpage.com for example.

Very simple to use and works perfectly.

Works exactly like I want! So flawless! I am picky because so many add-ons I have tried did not work as smoothly as I had hoped. This did the steps perfectly even though I was doubtful at first. Thanks Tom!

Uses external service file.io
I expected this to work completely offline, but it uses external service, which does have its own Terms & Conditions and Privacy Policy, by the way. Just read the source code of the addon, and T&C with PP of file.io to see if you're OK with that before using this addon.

So cool!
I thank you in (almost) all languages of the world.
شكرا, շնորհակալություն, hvala, gràcies, 谢谢你, hvala, děkuji, takker, hartelijk bedankt, thanks, aitäh, kiitos, kiitti, merci, გმადლობ, გდმადლობთ, ευχαριστώ, धन्यवाद, köszi, takk, makasih, grazie, どうも, អរគុណ, 고마워, paldies, Благодарам, takk, تشکر, dzięki, obrigado, mersi , спасибо, хвала, vďaka, hvala, gracias, tack, ขอบคุณ, teşekkürler, Спасибі, cám ơn, …

:-)

Great. It coud be useful to have a contextual menu with right clic on the search box of the websites to add it more easely to the custom search engine. Have you thought to do it?

THIS IS PERFECT! This is the ONLY thing keeping me from switching to Firefox from Chrome, and I wasn't able to find it a week ago. Now, it is here, and it works just as well as Chrome. I can type my keyword, then hit the spacebar, and suddenly I'm searching in my Google Custom Search Engine.

FANTASTIC WORK, MR SCHUSTER!

GOOD

Seems very useful...
Just a problem (solved by last update: thanks):
With Waterfox , the addon icon is not visible (just an empty square)
In Firefox Quantum, that's fine.