So I want to know if there is an implementation of Bitcoin where I can just start with a pruned node. I will sacrifice the security of verifying the entire chain from genesis for the convenience of just downloading what is necessary to construct a pruned node.
Yes there is, the category is called SPV clients and the example of it is
Electrum.
In this category, you download a very small amount of data known as block headers and perform minimal verification on a lot of things. Your communication with nodes will also be minimal each time you want to synchronize.
I just want to run a full node where I can just type in a certain public key, and it tells me which UTXOs are associated with this key
Maybe you should first explain what it is you are trying to do exactly.