Likely your tree’s root growth has created a large enough base for the tree to feel confident in creating a canopy. If the roots are not in a position to stabilize the tree, lateral branch growth would cause the mangrove to become too heavy and fall over.
I don’t feel it has anything to do with intensity of lighting but the more light given to the mangrove could help with the energy production to its root system.
If you look at your mangrove from the Birds Eye view, you’ll see leaves that alternate. Think of a clock. You have leaves in the 12 and 6 position and 3 and 9 o’clock position. If you want your mangrove to branch out in the direction of 12 and 6 you will find a pair of leaves in that orientation and cut the trunk a quarter to a half inch about them. New branch growth is typically produced just above the 12 and 6 orientation leaves right above the connection node of the leaves to the stem. You can do this the same for the 3 and 9 o’clock orientation. You can actually see it pretty well in the pictures you just posted. I use basic pruning tools you can get at the local hardware store from the garden section and just disinfect with some alcohol to make sure I’m not transferring any diseases. This is a fun alternative to trying to shape the main trunk with bonsai wire to create different shape. This doesn’t replace bonsai wire though. As the new branches grow in, you want to use that wire while the branches are still easily movable. Once they get the woody growth/ bark it’s harder to manipulate. I train the branches so that pockets of light from my LEDs mounted high up above the tank and trees can still get light in areas down to corals. Just like in the wild. There will be shady areas and bright areas of the tank.
*disclaimer: if you cut your mangrove, do not expect instant branch growth. Some mangroves do respond quickly to cutting, others it could stunt their growth similar to a stress factor like moving them to a new tank. I have had mangroves where cutting them has shifted energy to other locations of the tree, like growing larger prop roots. Eventually it’ll come back to canopy growth but it may take some time. I actually enjoy seeing this shift happen as a stronger root growth creates better stabilization for the canopy and the tree will respond with branch grow in due time. Again, my recommendations here are based on my experience and every result could come out differently. I know mangroves are delicate and should be treated carefully when in saltwater systems, especially their root system, but the leaf and branch canopy…. I usually hack mine back like a shrub probably twice a year. Only trim mangroves that are healthy. If your mangrove is dropping leaves excessively or you’re seeing any wrinkling, dark coloration or squishiness to a slight pinch on your mangroves trunk, DO NOT CUT THEM. You will only cause more stress to the tree.
Let me know if you have any other questions. I’ll see if I can get some pictures of my mangroves to help show where I would cut. I just recently pruned back my trees as they were growing into my lights.