As I understand it, BankID in Sweden is still run by one organisation co-owned by the big banks, and banks handle verification for issuance. There is still a single point of failure for the operation of the system.
I was under the impression that all of those services and login methods rely on suomi.fi in the end, but I admit that I don't understand the system terribly well.
No. As I understand it the previous system, NemID was actually (co?)designed by the banks so this is what they all use. Likewise MitID is another unholy alliance of Nets (a Danish payment provider) and Danish banks.
Given the Swedish version of it is called BankID I assume the situation is nearly the same in Sweden.
No. Many/most of them support login through hardware ID on your smartphone (i.e fingerprint/TPM-style pin), but the actual authorization of transfers or any privileged access is entirely MitID