For splitting the app in the taskbar I found it useful to “install” the PWA (you got to find the hidden option in chrome for that…), if it’s supported by the website… It still uses the same cookies and addons, but at least it doesn’t easily get merged with the main browser window and behaves like a proper desktop application. I mainly use firefox though and it doesn’t support PWAs (easily, at least). It’s a shame it’s not more common, because it’s a much better way to run software than the many electron apps, each having their own chromium installation (no download, no long installation process, full sandboxing, and you can have addons & adblockers affect the pwa!)
There are some surviving national circuits like PagoBancomat (as the sibling comment from Scrollone) and Dankort (Denmark) and girocard (Germany). My personal impression is that they are slowly going out of fashion in favor of visa/mastercard only (probably because they can’t offer better prices than them).
I don’t see a solution to the duopoly, apart from lobbying politicians to support this national payment infrastructure. Especially in recent times I can also see how some governments might not want to rely entirely on two US companies for running their entire economy, so something might move on that side, so there’s hope on that side.
The EU has already been moving on this front in the last years by forcing the banks to provide programming interfaces to initiate bank payments, and that’s why you can now see more and more options to “pay by bank” online in EU. These online payments generally skip card circuits and run over normal SEPA bank transfers.
More info here on the last part: https://en.m.wikipedia.org/wiki/Payment_Services_Directive