Some context: I'm French, I live in Belgium. I have two e-IDs cards: one french, one belgian. When I need to identify myself, depending on the government I have to deal with, I have to use either my "FranceConnect" credentials, or my Belgian e-ID card.
When using my Belgian eID, there is a government login called CSAM, but a lot of people here use a private company called "itsme" (https://www.itsme-id.com/). ItsMe does not support Linux. CSAM does, but not every service that supports or even requires eID login here supports CSAM.
FranceConnect is even more of a mess. French government has a plethora of online services, several with their own logins and not all support FranceConnect.
Making a digital wallet won't increase surveillance... surveillance is already possible on all of this, quite easily so. What it will do is greatly simplify life for people dealing with these systems; especially for expats and new arrivals into a country, who might get stuck in the loop of "You need a bank account to get your ID" "You need an ID to open a bank account"
Not to mention all the services that do their own shitty KYC and would be better served by using automated ID checking instead. Unless you think it's better and "more private" to email a photocopy of your ID and passport to somebody who will forward it three times, save it on their computer, and share it on Slack with the tech team because there's a problem with their shitty KYC system.