If I have a command block (of any of the three types)  and set it to conditional, and use the pick block with NBT (Control+Pick Block), the item will have properly stored the command (stored inside the tag Command, takes a String), stored whether or not the command block should trigger upon being placed (auto, boolean, or "Needs Redstone" is set as "Always Active"), stores that you do or do not want to track the output (TrackOutput, boolean), the times executed successfully (SuccessCount, int, which only stores a "1" or "0" in my checks) and also stores if the command block was powered before it was "picked" (powered, boolean). There is a tag, "conditionMet" (boolean), but I can't seem to figure out what it does. All of this information is stored in the item BlockEntityTag (Item:{tag:{BlockEntityTag:

}}). I do not know if the last tag is meant to store the boolean for conditional or not, or if it is stored correctly but not seen when it is placed. The boolean for conditional does not seem to be written in the block's data either, as I had two identical command blocks, but one was conditional, the other was not. I checked the blocks' data, and they seemed identical (aside from the x, y, and z tags).

All of the information about the items was collected using /data get entity @e[type=item,limit-1]. Similar for blocks, I used /data get block X Y Z. I have given as much detail as I have gotten, and hope this helps and gets fixed!