How do smaller military elements grow in size?

The force structure process is incredibly complex and detailed, way more than you might think on the surface. It deals with not just personnel authorizations (spaces) and actual people assigned (faces) but as you drill down it involves service schools for the impact on students loads ( more or less soldiers of various MOS needed) , the rank pyramid of an affected MOS, the impact on recruiting quotas, plus all the issues of equipping the new unit. It gets really really complicated.

But in general it starts with the need to justify why this unit needs to grow. Was there a change in unit mission, or doctrine or operational concepts that justify the change? A commander can't just say he wants more engineers. Then, a huge issue is who is the bill payer? If you get 100 more spaces, someone has to lose 100 spaces. Depending on how i portant the Army considers the change, they may direct your major command to take it out of hide and ID bill payers within your command. Or they may say that it is so important that they will task another command as the bill payer.

If approved as a concept, it will take years to fully staff and change MTOEs involved. So often they will create provisional units, where they allow one command to rearrange their structure internally before all the paperwork is done. I'm not familiar with NGB processes, but I would imagine a force structure change in the Guard would still have to go through the pentagon and the overall Army force structure process. Because as I mentioned, if you want to change 100 clerks into 100 engineers, that affects the engineer school loads which could mean they need more instructors or classes or equipment. So it's pulling on a ball of string that never ends.

So my guess is that ultimately it would involve approval by both the NGB Chief and the Chief of Staff of the Army.

I would guess the final decision/approval is done at the National Guard Bureau level, with State TAGs as key members of the discussion. Some changes may be trades/swaps, while some may just be based on NGB numbers.

Really hard to say, since there are a several things that might have happened. I know in my state for example, we've traded a quartermaster company for a special forces company between states. That's always a possibility, again really hard to say where and why the move happened.