I was trying to keep it short and simple by skipping a step but yes, the SSA follows a formula to raise the cap. But anything the executive does must be authorized by Congress, including the current formula which was set in a reauthorization bill back in the 80s (I think, maybe the 90s, apologies, but I’m not able to look it up right now). So far, every time a budget is passed and every few years when the SSA needs to be reauthorized, they’ve left them alone. Despite the occasional bill messing with the SSA getting introduced, they never get out of committee.

As far as the CBO goes I don’t recall ever reading about cap increases in their report summaries. I’ll have to do some more looking when I have the time, but I was definitely under the impression cap increases were in a category the CBO didn’t anticipate future changes to. I thought normally the COLAs would also fall into this category but that is overridden buy them being mandatory spending, as opposed to discretionary, so they have to be taken into account. I’m certainly no expert and wouldn’t be surprised to find out I missed something.