Genuine questions here so forgive me if they sound trite
1) aren’t all public addrrsses available via blockchain? This includes ballet ‘virgin’ bitcoin such as the recent .00325 slabs they were selling.
I think you are confusing the address and the public key. It is possible to compute the address from the public key via hash functions, but quantum computing can't derive the public key from the address.
The threat of quantum computing, is that, these computers might be able to derive the PRIVATE key from the PUBLIC key, via shor's algorithm.
2) How do we know that the website you provided isn’t compiling addresses once we ‘check’.
In fact, the website already list all the vulnerable addresses. It is something public.
I final note though, if after entering an address, you see something:
0 BTC compromised
I think that it does NOT mean that this address is safe. It is just that the balance is displayed as an integer...
Therefore you may have something like 0.7 BTC unsafe...
Hope it helps