I think anything that is not cage could be a toy - if you have edible perces from willow etc. they are not just for sitting but also entertainment.
How many toys depends on the size of the cage imho.
Sunny is still getting used to cage-invading things at all so atm she has a few brances for gnawing, a treatwheel that is fouraging and doubles as a foodcup (so it more or less there to stay and will not be swapped) and a gym-like wooden contruction she is scared to touch unless I hold it for her ...
Appie has 4 (ladder which she loves to destroy and all natural huge applebranch/small tree, a wooden-swing-gnaw thingy and one of mostly rope, and (not in use because it might kill her or something) one of those fourage acrylic-toys -> which is new and will be ignored for a few weeks at least.
Japie has 4 because I just removed anything cardboard from his side of the cage, 2 fouraging and one to swing from/ gnaw on, and his foodcup aka treatwheel (he prefers to eat from there...)
I do not swap as fast as every 2-3- days, they all need time to get used to toys anyway - only Appie came with a few toys and I do not think the other 2 ever learned to play with toys before they got here.
And of course they roam about the house, so *anything* is a toy (unfortunately for me ;P )
As long there is space for the bird to actually still flap his/her wings and get from one side to the other ...
(while I am typing this Appie is doing upside down gymnastics with one foot holding on to a fruitspear -> so I guess that counts as a toy as well? )
Yes as stated above it really does depend on the size of the cage. You want to give them enough room to stretch their wings, but also not bombard it with so many toys that they can't get around. Here's two sides of the double flight cage I have, one cockatiel in each.