‘Longtermism’ just says that improving the long-term future matters most, but it does not specify a moral view beyond that. So you can be longtermist and focus on averting extinction, or you can be longtermist and focus on preventing suffering (cf. suffering-focused ethics); or you can have some other notion of “improving”. Most people who are both longtermist and suffering-focused work on preventing s-risks.
That said, despite endorsing suffering-focused ethics myself, I think it’s not helpful to frame this as “not caring” about existential risks; there are many good reasons for cooperation with other value systems.
Thank you for your input! I agree with the point about co-operation with other value systems.
EDIT: as MichaelStJules pointed out, I think I was also mixing up existential risks (a broader term) with extinction risks (a narrower term).