The spore drive is not available for escape, because it is being used
as part of the apparatus to recharge the time crystal that was provided by Po. This will render the spore drive inoperative while it is charging and for 12 hours afterwards. This process also makes the time jump a one way trip.
As for why they can't just jump away to some far away location before starting this process, they could, and that would be a sensible thing to do, but that introduces a new problem with canon continuity:
Not everyone on Discovery can go on the trip to the future, e.g. Pike and Spock need to stay in the present, for this season to make sense. If Discovery spore jumps to some far off location, then Pike and Spock have no way to get back to where they are supposed to be. Hence, Discovery is effectively limited in how far away it can jump by how far the Enterprise can travel. The Enterprise appears to be only slightly faster than the Section 31 fleet.
So, it's a contrivance on the part of the writers, but one that turns out to be very logically necessary considering that the actual goal they have for this season is to ultimately fix all canonical problems.