Well calling it a whole genre is a bit of a stretch. Mark Sandman of Morphine coined the term “low rock” for their type of music and there’s a couple bands heavily influenced by them that also use that label. Monique Ortiz makes music that continues the low rock vibe, and then she’s collaborated with Morphine’s drummer on Bourbon Princess, and put out an album with Morphine’s saxophonist as “A.K.A.C.O.D.” And there’s also the band “Twinemen” with former Morphine members.

these are kind of micro-genres since there’s only a few bands playing in these styles:

• brass house - saxophone-based dance rock. Moon Hooch, Too Many Zooz, and their combined side-project Thundersmack.
• low rock - sax and bass guitar jazz rock style originated by the band Morphine, and continued by Monique Ortiz and the band Bourbon Princess