Available means not currently on any team's roster in your synced league, checked against every team, not just yours, so this never suggests a player someone else already owns.
Your roster's needs are computed the same way the Trade Calculator and Trade Finder compute them: for every position, how many startable-quality players (positive VORP) you have compared to how many starter slots you actually need to fill, accounting for FLEX/Superflex eligibility. Available players at a position you're thin at get a boost; players at a position you're already stacked at get a slight discount, so the list reflects your actual roster, not a generic ranking everyone in the league would see the same way.
Kickers and defenses are ranked by Rest-of-Season Edge Score alone (streaming matchups isn't really a "need" the same way skill positions are), while QB/RB/WR/TE get the full needs-boosted treatment.
A small secondary bonus is added for real Sleeper trending-add activity: how many leagues across all of Sleeper have added this player in the last 24 hours. It's a tiebreaker on top of the needs/Edge Score ranking, not the main signal, the same way market ADP is a secondary bonus in the Trade Finder rather than the primary driver.
Always prefers real Rest-of-Season projections over the static preseason numbers, same as the Trade Calculator and Trade Finder.