In the past week I myself and many people I know were not able to receive a USD wire from US to their accounts in different Russian banks, none of which are even in the list of sanctioned entities (Tinkoff and Avangard banks are the most common example). In all these cases the transfer was declined by a US bank, probably due to compliance considerations. Sending USD or EUR outside doesn't work either, and in some cases you cannot even exchange the remaining USD on your account to RUB. The options are indeed available in the bank's web or mobile application, but clicking 'Send' just gives you a 'something went wrong' error and that's it.
It is true that Putin might be not noticing any inconvenience, just as most employees of state-owned companies (who happen to be the core Putin supporters), but people who rely on international payments for living (who happen to be the least loyal to Putin part of the population) are being severely hit by the sanctions and have spent the last week in the state of permanent panic trying to figure out what are the remaining options they have and how they'll pay their expenses in a month from now.
Also, got bless crypto currencies! It would be not that easy to shut down P2P withdrawals until the internet is working at all. I have to admit, I was a big crypto sceptic right until the moment it became the only way to get paid. Now I'm a believer!
Not all banks are affected, only the most popular ones, it seems (e.g. VTB, Open).
All of them, including the "unavailable" ones, still have USD and EUR transfer options open to use, not sure if they are SWIFT-based or using something else now.
I don't know what's going on, perhaps DDoS from Anonymous or an overreaction from the banks themselves, but I'm pretty sure Putin hasn't even noticed this unavailability. Are they sure they know what they're doing?