however something that strikes me as counter intuitive is how PBKDF can somehow "stretch" the entropy of a supplied password to generate crypto graphically secure keys.
PBKDF2 and other slow KDFs don't increase the actual entropy, but increase its effective entropy. That is, a KDF can make a weaker password with relatively low entropy take as long to attack as a password with slightly higher entropy. Let's say you have a password with 50 bits of entropy. This means it has a keyspace of 250. If you halve the speed of the password hash by using two hash iterations instead of one, the keyspace stays the same, but the effective difficulty of cracking it has increased by one bit, to 251. Double the number of iterations again, and now you have the effective keyspace of 252. If we use 65,536 hash iterations (equivalent to doubling the number of hash iterations 16 times), we've increased the effective security by 16 bits. This would mean cracking your 50-bit password would require up to 266 hash operations instead of 250, making it as difficult to break as a genuine 66-bit password.
how does "hdk3mnt4k%@^" (a reasonable password), get stretched in terms of entropy by a PBKDF to generate a 256bit Sym or Asym private key?
I think you may be misunderstanding the purpose of PBKDF2. All it does is force an attacker to perform more work for each password guess than they would have to otherwise. When you're turning a password into a 256-bit key, you aren't actually increasing its entropy to 256 bits, just increasing its size. This can be done by any 256-bit cryptographic hash algorithm, whether it's a KDF or not. A hash algorithm takes an input of arbitrary size and generates an output of a fixed size. It is designed such that it is computationally-impractical to discover an input that hashes to a specific output, and it attempts to ensure that each input has a unique output (within the limits imposed by the pigeonhole principle).