How long does he complain for before he either finds something appropriate to do or starts being naughty for attention? How does he react to being given genuinely useful jobs to do?
I find it's good to let them be bored and not give in to screen time demands (not too much anyway) but some children become destructive left to their own devices. Seems especially so without siblings, DS1 was terrible for it. DS2 is ten years younger (nearly 7 now) but has DS3 to play with. He will often find something to play with DS3, but if there's too much unstructured time he goes into the attention seeking mode and we start bickering at each other.
If you have too many toys it can be hard for them to see what they have. Having a clear out or even just a sort out putting things into themed tubs etc and weeding out the broken, lost, outgrown things helps. Anything that consists of dozens of small parts that doesn't work when enough of them are missing I find it helps to keep in a self contained kind of container, like board games are, and have a designated pot for lost or stray parts, so when you find one in the wild you don't have to look for the right box. You can get him to do this with you under the guise of rearranging his bedroom or making space for (specific wanted toy) or making space for a sleepover or to repaint a wall or something.
Also looking for new ideas for how to use your existing stuff is good. Rebrickable is the best website for Lego, if you have a computer he can use I'd get him sitting with that and looking for new things to build. He can put in what sets he already has, and it will tell you what bricks you have and suggest things to build with them. Or get one of those big books of activity ideas, or the dangerous book for boys, simple science experiments to do at home, anything like that. The library will probably have some (they also have things like drawing guides, Lego ideas, teach yourself XYZ) if you don't want to spend money.
If this is not enough, the best thing I've found is to get them started. Spend a couple of days literally just sitting and playing with them following whatever random idea one of you has and when you get bored, tell them ok five more minutes then I'm going to do the washing/lunch/have a cup of tea and a sit down. If I dedicate a couple of days to it I don't feel as frustrated at not having time to do other things.
The more you do this the more they get used to doing their own activities, and I find if I spend a bit of time playing with DS he will then continue the same kind of activity without me, much more so than he would have done if I'd never done it at all. I used to avoid this with DS1 because I felt like if I played with him a bit it was all he wanted to do but I've got into a better rhythm now with DS2 where I play a bit, then do my own thing for a bit, then I might come and look and admire what he's doing, then he'll get bored and do something else.
You might want to also try a bit of bribery. Get him to come up with or choose from a set of ideas of something to learn and if he reaches certain goals he can have some money to spend or a trip out to a specific place etc. Kind of like the library reading scheme but make up your own goals together. Good if he has input into it rather than it just being you leading this, but you'll probably have to be the structure for it.