Can I use Absol's "Drawareness" Ability to discard until I only have 5 cards in my hand and draw nothing?
No, you aren't allowed to discard any cards if it doesn't result in you having 4 or fewer cards in your hand. For example, you can't discard down from 6 cards to 5 cards; you would have to go from 6 to 4 at least.
Source: Paradox Rift FAQ; TPCi Rules Team (2023-11-02)

Relevant cards

Note: All applicable cards may not be listed below.
SV4_113
SV4_113