Oh yes, and I forgot to mention that you access the Blue Spheres stages through checkpoints in Sonic Mania. If you have 25 Rings or more when you pass by a checkpoint, a halo of stars will appear above it. Jump into the stars to get to a Blue Spheres bonus stage. Now, I'm not sure if it's an oversight or it's intentional, but hitting a checkpoint and entering a Blue Spheres stage will reset any checkpoints you've hit prior in the stage, so if you can go between checkpoints, you can access these Blue Spheres stages as many times as you like. (And you don't lose your Rings along the way.)

Like in Sonic 3 & Knuckles, you play these in sequential order, which is why I know the order of these Blue Spheres stages. If you haven't cleared them all yet, the game will skip any you HAVE cleared. If yo've cleared them all but haven't obtained a Perfect in all of them, it will skip the ones you have a Perfect on. And if you, like me, got a Perfect on them all (though I didn't do them all in one try), it'll just start over from Caramel each time you start up the game and not skip any.

I explained the rules to the Blue Spheres bonus stages in the Part 29 video. Blue Spheres is definitely a mini-game you're not meant to jump in blind, as knowledge of the rules makes them much easier. Well, that and I played Sonic 3 & Knuckles to death back in the day, and Blue Spheres is knowledge I haven't lost.

STAGE 9 - HARLEQUIN
(Sonic & Knuckles - Special Stage 3)
Blue Spheres: 72
Rings: 64
If you played some of the ones before this one like Ahri and Mint, you should be familiar with the partially completed clusters of Blue and Red Spheres that can turn into Rings. Actually, I thnik this one is meant for you to accidentally stumble across them.

STAGE 10 - BROCCOLI
(Original)
Blue Spheres: 136
Rings: 68
There isn't anything that out of the ordinary in this one, but it is rather long (despite all of the Blue Spheres stages taking up the same amount of space). Remember that your character walks faster and faster as you spend time in these stages, giving you an incentive to clear them as quickly as possible, though it does max out at about 75 seconds.

STAGE 11 - CIRCUS
(Sonic 3 - Special Stage 4)
Blue Spheres: 115
Rings: 80
There is a large plus-shaped cluster of 44 Blue Spheres here that can all turn into Rings by going along its perimeter. Otherwise, due to the unusual paths and bumper spheres next to Red Spheres, it is very easy to fail this one by timing your turns and jumps wrong.

STAGE 12 - HONEYCANDY
(Sonic 3 - Special Stage 5)
Blue Spheres: 58
Rings: 54
I called this one what it is as it reminds me of Violet Crumble. Ever had any of that candy bar? Yeah, I kind of got lost on this one, but I still made it through. There are only 4 Blue Spheres here that don't turn into Rings, so make sure you get those ones last for the Perfect.

STAGE 13 - LAVENDER
(Original)
Blue Spheres: 74
Rings: 58
This one introduces you to a more complex  formation of partially-surrounded Blue Spheres, which requires you duck in and out of the perimeter. Otherwise, there are some pretty dense formations of Ringable Blue Spheres with un-Ringable ones that demand some pretty good timing once you really speed up.

STAGE 14 - SEASCAPE
(Sonic 3 - Special Stage 6)
Blue Spheres: 128
Rings: 64
This one is a very straightforward one, consisting of four 4x4 formations of Blue Spheres that make up the 64 Rings to find here, connected by straight corridors 2 units wide with a 2x2 set of Blue Spheres at each end making up the remaining 64 Blue Spheres. That being said, it's up here for a reason: As it's very nonlinear, that means you'll likely need to jump over those 2x2 sets that have been converted into Red Spheres. Better practice your jumping. (I didn't. I got lucky.)

STAGE 15 - ARCHIPELAGO
(Sonic & Knuckles - Special Stage 4)
Blue Spheres: 155
Rings: 64
Say, don't you get the feeling that the Sonic & Knuckles set is a step up in difficulty from the Sonic 3 set? Makes sense though, as Sonic 3 & Knuckles has the Sonic & Knuckles set come right after the Sonic 3 set. In any case, this is the first Blue Spheres stage in the game in which EVERY Ring is out in the open, and none of the Blue Spheres can be turned into Rings. As this stage's Blue Spheres are entirely found in paths with Bumper Spheress on the immediate right and Yellow Spheres on the immediate left, that means you have to go into the middle to get the Rings, then jump out and continue what you were doing before, then jump over a former Blue Sphere to get onto a Yellow Sphere to move on to the next set.

STAGE 16 - WOLFPACK
(Original)
Blue Spheres: 127
Rings: 101
Here's another one where there are more Blue Spheres than the amount you're asked to get, which I find is weird. All of the ones found in Sonic 3 & Knuckles required you to collect them all. It's very linear, but don't forget to collect the Rings out in the open that guide you along the optimum path.