The complaint is about Apple not allowing 3rd party usage of their NFC chip for other wallets (or anything else for that matter. From my understanding, the access is very limited) :
Quoting :
As a result, users of Apple devices can only pay with the ‘tap and go' function using Apple Pay and not with other wallets. This is because competing wallet developpers need access to the NFC on Apple devices to reach Apple users.
Interestingly they also say that the Digital Market Acts will regulate this :
When it enters into the force, the Digital Markets Act will have a direct effect on digital payments. It will require companies designated as gatekeepers to ensure effective interoperability with hardware and software features they use themselves in their ecosystems. This includes access to NFC for mobile payments.
(IANAL but I find it interesting that they mention specific upcoming regulation tailored to curtail this, while still sending to Apple what they call a Statement of Objection)
My vague (and possibly completely wrong) understanding from the situation here in France is that banks have to individually sign up for this, but on the backend the payment processing is piggybacking on Mastercard/Visa payment network, as from day one, Apple Pay worked on everything (with some caveats) that accepted NFC payment (which most terminals did). Transactions show up on your receipt as (in my case) a "classic" Mastercard transaction.
This doesn't seem to be the way Apple Pay is implemented everywhere though (particularly in the US) ? This may be anecdotal but I had this discussion with a restaurant owner who mentioned that Apple Pay payments from some US customers didn't work (while in my case I've noticed eu/fr variant of Apple Pay worked pretty much everywhere). This could be some random other issue though.
It would be interesting to know if in other EU countries this is always the same, piggybacking on your bank/card network.
While I broadly understand the idea of opening up the NFC to 3rd party wallets, it's unclear to me how much of a practical idea that would be. As someone who uses Apple Pay daily, I don't see how having to open a 3rd party wallet app would be comparatively effective, it's all about the convenience of being able to triggering it instantly.
A better solution would be mandating/allowing those 3rd party wallets not only NFC integration but having their payment options showing up in Apple's Wallet so they can be triggered the same way (double tap on your iPhone/Apple Watch, which already lets you pick between various Apple Pay cards/QR codes you may have entered).