By the way - by tidying up - I don't mean that you need to be obsessively following them around with a dustpan and brush and shouting at them for dropping a single crumb, or having draconian rules about how many things they can have out at once. I just mean things like this have been helpful (to me).
Have a massive declutter - less stuff is much easier to handle for everyone. I've always been a messy person and I really like the podcast A Slob Comes Clean as she has helped me with a lot of things about this. Also you can watch Stacey's Sort Your Life Out on iPlayer which has a lot of episodes with young children which can be helpful/inspiring.
Downsize toys, and sort them so you don't have endless boxes of mixed things which are just instantly dumped out every day because they are looking for one specific item at the bottom of the box and can never find anything. Sort everything into individual boxes by type of item. You can do this slowly bit by bit if you don't have a lot of energy or time, just start with a box for the most popular item that they have (for my kids it would be toy cars, trucks, vehicles - even when everything is shuffled, I could easily empty out a drawer or box and fill it only with those). If you're doing it bit by bit, put any leftovers into any other "unsorted" box for now. Label the box with stickers, a printed out photo, or terrible drawing stuck to the front of the box with sellotape so that non-reading children can understand. Examples of categories that we have (my youngest are 1.10 and 4.10):
Balls
Cars/vehicles (matchbox/hot wheels size)
Animals/farm/dinos/fence
Chunky toddler cars/vehicles
Tools, construction
Mega bloks
Wooden train tracks + compatible trains
Doctor's kit, baby doll, accessories
Musical/sound/baby toys
Stacking, nesting toys
Kitchen stuff and food
Large vehicles (fire engine, rubbish truck, digger)
Get rid of things that are too little for them, put away for now things which the baby will chew or break. Keep board books accessible, put picture books and lift the flap books and pop up books somewhere higher.
Pare down duplicates or excessive amounts of anything (e.g. you probably want a few cars, but you don't need hundreds). Get rid of anything broken or that doesn't work properly or is always running out of batteries or that they find frustrating and abandon quickly.
Any items like shape sorters which are useless without all of their pieces, get rid of all but about 2-3 max, store the pieces inside the main part and put them somewhere they need to be asked for.
Toys which the baby needs to be supervised around (lego, marble run, colouring) store in a visible box that needs to be asked for.
Board games, puzzles, keep only the ones they actually play with and get rid of (or put away for when they are older) any which are just too annoying. Or you can rotate these out so only have a couple available at any one time, so the pieces can't get mixed up and lost constantly. Have a "lost pieces box" and any random jigsaw, game, toy pieces you find go in this box and when you need something you check here for it.
The point of doing all of this is that it makes their play a bit more focused and clear. You can instantly see that they are playing dinos, and the trucks that are on the floor over there aren't part of this game so they can be tidied up, and it only takes a minute because it's a few trucks rather than every single toy that they have ever owned. Or they are playing trucks now and the dominoes they got out earlier have been abandoned. Or maybe they are playing dinos get in the trucks and have a ride on the domino road - this is fine - but then the play kitchen stuff can be tidied back up. When they want to play trucks, they can just get the truck box, and they don't need to dump it out because it isn't full of random other stuff and they can see everything, so it's easier to put the trucks they were playing with back. When they want to make a farm, they can find the fences because they're in the same container as the animals, and they don't need to go galumphing through everything else you own to find them, and when they do find them, they all fit together because you've got rid of the odd non matching ones, so they aren't instantly frustrated and throwing a tantrum.
Another thing you can do if you want to is to rotate toys. Some people find this amazing and helpful and some people hate it. It doesn't work for me, but it can help a lot with keeping things fresh and exciting (which reduces them getting instantly bored and getting out every single toy) as well as reducing the volume of toys available to get out.
And when they want one of the items that's visible but not reachable, you say something like "Yes - I can get that for you, but first we need to clear a space." and then you know that it's out so you can keep half an eye that the pieces don't get abandoned everywhere and when they have finished with it you can put it away.
At first when you set this up you just tidy around them. Not constantly - just when you happen to notice one of the previous scenarios, go and pick up those trucks and put them back in the box. Go and put the kitchen stuff back in that box. Because it's only 1-2 category's worth at a time it takes a few seconds to put away (rather than the hours of tidying associated with general constant mess) and instantly they have more space, which they will get used to and come to value. They do not value this currently, because they are not used to it. They will probably be confused about why/what you are doing (and resistant if you try to involve them) if they are not used to tidying, but if you explain "I'm making you some space so you can play with your toys" they will soon start to see the benefit of this and once they do, then you can encourage them to join in. Even before they see this, start a nightly tidy up that involves everyone, showing them that the pictures make it easy to see what goes where. Praise them when they join in, make it a game, put a tidy up song on, whatever makes it fun. 1yos are great for this because you can show them and they just think it's a fun new game and everyone claps and cheers, and then the 3yo sees the baby getting praised and wants to show how well they can do too. Don't start this on a day they are brain-meltingly exhausted, and don't push it initially if they are pushing back, it's best to get a positive start rather than establishing it as a hated chore. (Once it's an established habit, then you can insist). But the adults should at the very least try to tidy up after they are in bed. Then you have a clean start the next morning so they aren't piling mess on top of mess on top of chaos when you haven't even had a coffee yet. You can even get one box out invitingly and place it in the middle of the room, which somehow often has the magic effect of enticing them to play only with that box of stuff for ages.