Do I understand correctly that mnemonic seeds are specific to individual wallet software and its versions? I know mnemonic passphrases are used to derive a master key that can then be used to procedurally generate your addresses. If you lose everything except the mnemonic, you can regenerate everything and recover your losses.

But from what I understand, and as my limited experimentation has shown, these mnemonic seeds seem specific to an individual program and even its versions.

So let's say one day I lose everything except my mnemonic and I decide to recover it all. I set up my a new pc and such, and look for a wallet program. My original program is no longer available because nyan cat ate the source code. Am I now not basically screwed because any alternative program won't be able to process my original mnemonic seed?

So if I want to not take any chances and not be bound to any single platform, I shouldn't focus on the mnemonic but on my master key, which I'm merely presuming is standardized and universal. Having to store this single long string of pseudorandom chars isn't exactly an improvement over storing a csv of pseudorandom strings, is it?

And of what I've seen, programs like even electrum and mycelium are all but crystal-clear about what exactly you are backing up and what exactly you can do  with it (on mobile - electrum is much clearer on desktop, though it still doesn't say anything about the nature of the mnemonic for example). A button labeled "back up my wallet" doesn't really tell me if I'm backing up either type of seeds or just a list of keys, or something else. I suspect a binary file specific to this wallet program at that moment. Programs relevant to the same thing (i.e. wallet programs) should really carry labels on all their features, pointing out what is universal/standardized/cross-platform and what isn't.
There are standards.  You would have to check that your particular wallet program conforms to them.

The standard for converting a mnemonic passphrase to/from a seed is BIP 39.  The standard for generating keys from a seed is Hierarchical Deterministic Wallets, BIP 32.