Depending on the depth and size of the pits, it may be feasible to just leave them as they are and recoat the surface, or to weld them up, or to patch or replace the tank. Normally, this would be evaluated using API-653 or similar methods.

Double-check the manner of construction. The outer shell may be non-loadbearing, in reference to the contained liquid, and the roof. It may just be there to hold in the insulation [not uncommon] If this is the case, you have the equivalent of a metal shed.

Fix it in a "workman-like manner", using normal repair methods for low-grade carbon steel. I would use A-36 for the patches, and probably weld with E6010, as that rod is very rust-tolerant [you never get all the rust out of the bottom of pits]. I woud be more inclined to use patches than welding up pitting, as it tends to be more cost effective.