we can look at real world examples from deserts, islands, where tree wood is very rare and cultures were bamboo is extremely common.
what is wood used for.
Ships, you can make a raft out of bamboo but you can't make a large water tight ship out of it without modern composite technology.
Axles, hubs, and bearing, even in places where bamboo is common and most of a wagon would be made of bamboo, axles and wheels were made of wood since bamboo could not be carved properly and still survive the high wear. Note for smaller hand carts bamboo will work OK and bamboo might still be part of a wheel, like spokes on larger wagons.
tools, The unsuitability of bamboo also extends to bearings for certain tools, like on lathes where they need to surround a spinning a shaft with a wide contact surface. Or pulley wheels, or vises, basically any large thick three dimensional shape that must be solid. The more technological the society and the more complexly carved a tool needs to be the less suitable bamboo is and the more wood for machine parts they will need, right up until the use of metals for such things can become common.
Plows, because of how bamboo is shaped, and how weak it becomes if you cross fit it, it is unsuitable for certain parts of plows.
on the upside these are all places were the wood can be used for decades before it wears out, so a little wood goes a long way. Expect them to favor hardwoods or rot resistant wood for harvesting, if it is dangerous to get they will want wood that last a long time when they do get it.
Bamboo can be used for basically everything else wood is used for bows, arrows, fuel, charcoal, construction, ect/ bamboo is actually better for some things, it makes ready made pipes and containers easily which is not true of timber.
Just to be clear you can get wood from cycads, they just grow very slow so wood is still valuable and not abundant. It is similar to palm wood so they might be able to make canoes out of it.
Also as others have mentioned pre-industrial paper is as more linen and cloth scraps than wood pulp. So your society still has plenty of paper. Modern paper making switched to wood pulp because it is cheaper, not because it is better.