Cracks in stuff, not just clay will it ever be crack free? That depends, you can stop a crack sometimes, you can fill a crack sometimes and you can make the crack a part of the design by carving it out or covering it up.
On the bottom of a complex piece where the bottom ‘s not visible from the inside or if like in your case the defect is only visible from the bottom, if the piece is glaze fired sometimes I will make a new base to attach with a low fire glaze to cement the bottom to the new base the new part can be fired to match the original artwork or complimentary but different. Attaching the two pieces at a firing temperature well below the original firing temperature puts less stress on the clay during the latter firing. Heck the new UV light activated polymer glues work great attaching the pieces together too on decorative items.
stopping a crack if it is complete is key to dealing with a crack, this involves at a minimum drilling a small hole at the end of the crack at both (all) ends this distributes the stress contained within the clay in this case over a greater area stopping the crack from running and then carve out the crack into a v shaped depression for later filling. After the crack is stopped by relieving/redistributing the stresses the crack can be carved out and made into a design element, covered with a sprig or in the case of green ware slowly filled with multiple coats of paper clay slip sanding the surface when dry to match the artworks surface.
Epoxy putty and acrylic paint is another useful item for restoration work, the putty I’ve used has been pure white and sanded has a silken texture similar to porcelain, I imagine it can be colored with stains as well as painted. I’ve restored Chinese porcelain filling cracked broken areas and by making new parts with latex rubber molds made off intact similar objects finishing the parts with a jewelers flex shaft and small carving bits, cementing them in place with more putty.
will these tips always work, probably not but if done carefully I’ve had success more times than not and rescued hours of work, you need to decide if this works aesthetically for your piece.
One more thought, use a Dermel tool and diamond bit and carve the crack into a signature or an intentional mark if you are lucky enough it has taken a shape you can use and have the skill to control the tool.