I'd categorize SWADE as a system as strong for non-combat roleplaying. Of the 12 TTRPG rules I use, I'd group it among the better 3 with FATE Core being the best.
As dbm and others have already mentioned, there's a number of gameplay mechanics that support encounters other than combat. But a clarification 1st; Quick Combats has been mentioned, but that was the older term when the play mechanic was 1st introd as an addendum to the SWD version of the rules. In SWADE it's referred to as Quick Encounters and the book highlights these 6 types - chase, combat, heist, crisis, mission and trek. There's a Social Conflict play mechanics that's already been mentioned, but I've at times instead used the Quick Encounters framework for social encounters. The same is true for Dramatic Tasks, which the SWADE details for Social Conflicts mentions as an alternative approach to handling social encounters - better when the pressure of time is a factor.
Another thing that's often overlooked is how a PC's Hindrances can potentially be brought into play. I frequently use them like you would a trouble aspect in FATE, or some other aspect. I also at times link into a PC's hindrance as a source for an adventure hook - mostly for a short adventure. There's an optional Adventure Deck that's available for SWADE, for which each card presents a nice boon - some of them situational. I typically use an adventure card instead of a benny as a reward at the completion of a hindrance-hooked adventure. You can employ hindrances for all sort of narrative play, if as GM you're mindful of the hindrances each PC has.
And as to bennies - the RAW says to award 3 to PCs at the beginning of a session, but there's nothing saying that as GM you could hand out fewer -say 2- at the start of sessions for which combat is going to be minimal, or non-existant.