This is not about the Keycard in the Quarters part to get into the cave leading to the HP filters, i've already been there and done that.

However there is a door within said cave though, that requires another key.

I've googled this and all that came up was the keycard for the filter quest, even pickpocketed Keely to find a passcode to activate her terminal which opened something (supposedly). Just can't seem to find a way to open this door in the cave, does a way even exist?

The door you are talking about is the cave side of the door on level 3 that requires the keycard; that door is sealed with an override that can only be turned off at the terminal on the level 3 side, which itself needs a key in the form of the card.

I thought much the same as you currently are the first time I got into that cave from level 5, since it's not obvious at first that said door is merely the other side of the one on 3 that you need the card for.

Oh I see.. so there's basically no purpose to opening it now anyways. Thanks man, that would have bugged me for awhile lol.