As part of my startup's remit, I do a lot of work with clients' SWIFT payments. I feel like the media has done a very poor job explaining what SWIFT is and how exactly it works.
SWIFT exists not for the purpose of providing the rail(s) upon which money moves but to be the messaging system which coordinates said transfers. When sending funds (typically done via a document called a MT103, which is a text file with specific formatting requirements) one informs the recipient institution by sending a SWIFT message. When it is time for the banks to actually move the funds (which often times occurs significantly after the funds are made available to the client in question) this will be coordinated through a payment system. In most cases in Europe, this is TARGET2. However, as Russia is not a member of the Eurozone, many of their impacted payments will likely be on the STEP2 payment network, which is the only European-wide clearing house. (However, these days, it isn't uncommon for banks to work together to use multiple clearing houses across multiple jurisdictions to most efficiently move funds.)
From what I understand from banks and clients we work with who have a significant Eastern European nexus, Russia was already experiencing problems with the payment systems before the formal SWIFT bans were announced and that the effective shutdown of central bank settlements for Russia has served to bring international payments coordination for RU based institutions to a crawl.
Happy to add clarification where it could be useful.
