Well, that's not false but I'd say that both "bieten" and "anbieten" typically mean "to offer, to provide". The use of the prefix "an" simply makes it smoother and unconsciously slightly more directed towards the person or entity which is being offered sth (here: customers). It's also much more common.
I think this is one of those regional things which sometimes surprise us. To me, I would use the term "Sale" almost exclusively for this. Sometimes you see "Special Offer" printed in a flyer, but to me that is purely advertising lingo to describe the sale and make it sound better. I would never use 'special offer' casually in a sentence, like "Look dear, at this special offer on toothpaste." Definitely would say 'sale' there.
But again, I might be surprised at how regional that is. I recently learned that what I call 'utensils' are called 'silverware' in another part of Canada and 'cutlery' in the rest. And what most of us call a 'hoodie' is almost exclusively referred to as a 'bunnyhug', of all things, in Saskatchewan. So, perhaps 'sale' is fairly uncommon...
I'm from the Western US, and we use the word "sale" to describe this sort of thing. Same as you described. I would never say "special offer" about anything. It should definitely accept "sale," if that word is common here and where you live in Canada. Is there any sort of way to get the attention of people who can actually get that changed?
Here's a page from a random Canadian store, https://www.long-mcquade.com/page/sale/. Note "PRODUCTS ON SPECIAL." I agree that "Products on sale" is equivalent. I'll even allow that it's probably more common than "Products on special." Both are valid in my opinion (speaking as a genuine Canadian ;) )
...the religious use is not the only use, no, maybe not. But I think we can say emphatically that offering would never be used to describe a good price on a flyer item! I'm sorry, but offering definitely gives me the picture of a slaughtered goat on an altar. If you showed me a picture of a modestly priced drill set and said, "Look at this special offering", I would snicker.
Some dictionaries beg to differ: https://www.collinsdictionary.com/es/diccionario/ingles/bargain-offer
Not a native speaker here, but I am assuming I can understand both German and English sentences, and "is it on sale" doesn't sound as an accurate translation, for it distorts the meaning of the initial German phrase. "On sale" you would normally say about the products included in a special offer, while the question corresponds to the offer itself, not to the product included. Say, you can read some ad running about good prices for some products and you ask "Is that a special offer?" not about the product, but about the offer itself, hope it makes sense. Again I can assume, that in NA stores you might not see "Special offer" ads, seeing usually "On sale", but it doesn't make the latter a valid translation of the phrase given. It's just about custom formulas varying between the countries. Say in Russian or Ukrainian shops you normally see "Sale" ads at the boutiques, so it's mostly about the clothes and maybe accessories, while "Special offer" is more common in other cases(food, furniture, home stuff, instruments and appliances).