The military is not going to take action until it is absolutely necessary. Yes, the military is sworn to uphold the constitution, even over presidential rule but it's also well understood that a military coup should be avoided at all costs. Once initiated you cannot undo this. It has significant repercussions and has significant risk of starting a civil war. It is not a thing that starts one day and ends the next. It is a thing that at best last weeks, likely lasts months, but could last indefinitely.
It is also worth mentioning that the military is not a uniform and monolithic entity. If you're asking what arm is on the other side of that civil war, well it was originally part of the one the initiated the coup in the first place.
Trust me, no one wants a military coup. It should not be a tool used lightly. Do not ask for this until all other options have been exhausted
So far, their actions are compatible with both hypotheses.
It's when the orders come in to directly use military force to support unconstitutional acts that we find out, not simply when the military fails to intervene in legal disputes.