So I don't think anyone has properly explained Mach Speed Sections before so here I go:

Okay so there are three speeds you can have while in a Mach Speed Section:

1. Starting base speed (happens off start no matter what direction you're holding, will revert to this speed after: being hit in any other speed level, after taking a jump panel, not holding a direction for too long in any other speed state) - you can tell when sonic has this by looking at how far out he extends his arms

2. Increased speed (happens after holding forward while in speed level one for long enough, or if you hold forward off a ring dash, will revert back to level one if you stop holding forward or take a jump panel or get hit) - is significantly faster than level 1 speed, you can tell when sonic has this when his arms are behind him and not out wide

Both of those are intended by the devs The subtle glitchy one is level 3

3. Speed Cap Break (happens immediately after ring dashing if you don't hold a direction on the control stick) this one is a spectrum, it happens because ring dashing is faster than level 2 and the game forgets to cap your speed when you don't hold a direction on the stick. Thus, if you don't hold a direction out of a ring dash your speed will start at level 3 and descend slowly to two, once it gets to two, if you still aren't holding a direction it will revert you to speed one. This slow descent from 3 to 2 is because sonic gradually loses speed on the ground, you can sort of solve this problem by jumping since sonic does not lose speed while in the air but jumping all the time in mach speed sections usually isn't the best idea.

As for a visual cue for if you have speed 3, there isn't one, its sort of a feel thing, if you want proof that its faster play radical train and use speed 3 while chasing the train, you will almost catch up to it before the game realizes and makes the train accelerate.

"OK trips how do I use this to my advantage to go fast?" you say. Good question, complicated answer.

The general way to use speed 3 to your advantage is, whenever you get the chance to ring dash, do it and don't hold a direction immediately after for a little bit. This isn't always the case, especially in places where you're prone to get hit right off a ring dash or if you have to go ridiculously out of your way to get a ring dash but in general we try to ring dash as often as we can.

This is made even more troublesome because in speed three you will not be able to turn (because that would involve holding a direction). That makes it very difficult to keep speed three going often, as there are usually a lot of obstacles in mach speed sections and above all else you really don't want to have speed 1.

For example, in places like wave ocean, we do a lot of short speed 3s, we will ring and not hold a direction for just a little bit and then turn before we are reverted to speed 1 so that we keep speed 2 while also getting to the next closest ring trail, it makes the routing quite interesting.

Arguably the biggest time saves from speed 3 usages are in Radical train right before you chase the train, with a well timed jump you can stay in the air for an extremely long time while in speed 3 thus keeping you at max speed. It is very easy to see how much faster this is when you see the train shoot forward, not expecting you to be going as fast as you are.

If you're wondering what the best mach speed routes are to maximize the usage of speed 3, watch sharu's WR runs on Radical train wave ocean crisis city and kingdom valley for reference, these runs are all very recent and have fantastic mach speed strats.

Wave Ocean: Crisis City: Radical Train: Kingdom Valley:

Some of those strats are pretty tough and there are parts that I personally have not yet tested for consistency (namely using the cave in Wave Ocean and pretty much everything about Crisis City. If you want strats that I can guarantee are consistent then watch the 59:46 No MSG run's mach speed sections.

Having good mach speeds is a very subtle thing and takes a decent amount of practice but I guarantee it will save you at least 30s maybe more if you understand the mechanics.

A few more notes:
- Ideally you should always have speed 2 when you don't have speed three, HINT: THIS MEANS HOLD FORWARD THROUGH THE ENTIRE MACH SPEED SECTION, the only time you should spend not holding forward should be during and immediately after a ring dash.
- In Crisis City having speed 3 means things will fly at you with more velocity than is intended, this means they are prone to flying in more random directions and hitting you, which would take you back down to speed one, thus screwing you over pretty hard. As a newcomer, not dying in Crisis City is your number one priority so as a default I would just try to not get hit as much as possible and ignore using speed three. Being at speed 3 is only a bit faster than 2 but 2 is WAAAY faster than 1, so avoid being in speed 1 as much as you can. This means immediately after getting hit (which you definitely will eventually), you should find a ring trail ASAP and get back up to speed 2. If you keep doing that and stay at speed 2 for most of the time, you should have a decently fast mach speed time. I still have yet to find a consistent route through crisis city that will allow you to maximize speed 3 usage while also avoiding getting hit. That being said, I have yet to test out sharu's new crisis city route, so that might turn out to be consistent, who knows.
- Being in speed 2 makes it more difficult to get the Jump at the end of Wave ocean (the timing is more strict), this gives you two options, either slow yourself down to speed one right before the jump panel or try to hit it with speed 2. If you try the first option you will lose time right before the jump panel and during the jump if you get it (since the jump itself will be at speed 1) but it will still save time over missing it. If you want to try the second option I've found entering the loop AS FAR AS YOU POSSIBLY CAN TO THE LEFT helps a lot with consistently getting the jump. Some people time their jump input but the more popular method is just mashing for it (which I recommend)

tl;dr - mach speed sections are more complicated than you think ;)