Here are some pages on Skyscanner which lists rules for bicycles on some airlines. The information is a few years old, but at least they're a good place to start if you're looking for information.
https://www.skyscanner.com/tips-and-...with-your-bike
https://www.skyscanner.net/news/airl...r-bike-onboard

I have a folding bicycle with 20" wheels, which can fit in a cheap $30 standard sized plastic ABS hard shell luggage under the 158cm maximum linear dimension. Using this as an example, I was curious and asked KLM and Air France if I would have to pay additional special baggage fees.

KLM won't charge extra fees if the luggage is under the weight and size limit.

Air France will still charge a bicycle fee, even if the luggage appears standard. I specifically wrote about "parts of an incomplete bicycle" that fit in 2 separate luggage, and they wrote back saying that I'd have to pay a separate fee for each of the 2 luggage. My thoughts were to pack the folding frame in the first luggage, and the panniers and wheels in the second luggage. So I'd look for a different airline than Air France when traveling with a bicycle. Ironically, KLM and Air France are parts of the same company after a merger.

I looked at a few other websites of different airlines, and many of them have similar rules as KLM, where the bicycle would be treated as standard luggage if they're under the standard weight and size limits, and well packed and protected.

I think EasyJet will always charge a fee for bicycles, but the fee is cheaper than the cost of a 2nd standard luggage. So it may actually be more economical to declare and pay the bicycle fee if you are checking in 2 luggage.