After seeing this Q/A on whether releasing a grappled creature increases your available movement, I am wondering a more general question.

Under "Your Turn" it states:

On your turn, you can move a distance up to your speed...

I also noticed that the Dash action specifically states:

Any increase or decrease to your speed changes this additional movement by the same amount...

But I am still unsure; how do changes to your speed which occur on your own turn, such as ray of frost, releasing a grapple, or longstrider, affect your available movement for that turn?

For example, if you have 30 speed and movement, and you use 10 movement and then longstrider is cast on you, do you now have 30 movement left or 20?

If you have 30 speed and movement, and you use 10 movement and then ray of frost is cast on you, do you now have 20 movement left or 10?

My other question here is not a duplicate because it did not specify that the changes to your movement were occurring on your own turn (the current answer there assumed they were not on your own turn)

The rules are not clear, but it is not based on a percentile

The most relevant passage seems to be the "Using Different Speeds" :

For example, if you have a speed of 30 and a flying speed of 60 because a wizard cast the fly spell on you, you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet more.

This shows that movement is not based off of a percentile. In other words, if you have 30 walking speed and 60 flying speed, walking 1 foot does not cost 3.3% of your movement, rather it costs just 1 foot of movement.

So it seems like changes that occur during your turn simply add or remove feet from your movement according to their description. Ray of Frost (a cantrip that could be cast as an AoO), would simply subtract 10 feet from the movement that you have left, Longstrider (cast on yourself), would simply add 10 more feet that you can move on your turn (if adding 10 feet would bring you to a positive number of feet left).

Using the same logic (and the accepted answer to this question), releasing the grapple would give you back the half of your movement that you lost did not originally have due to the "grappling status."

The Dash action just allows you do use your Action to move equal to your speed. Once again, it seems to just be based on what your total speed is at the time.

For instance if you have a speed of 30 and you move your full speed and take the Dash action, and happen to walk past a spellcaster with the War Caster feat, who casts Ray of Frost on you. If you fail the save, your speed drops to 20, and your total movement available to you that turn is now 40 (20 * 2 = 40), so you can only move 10 more feet.

The maximum distance you can move literally is your speed

There is no rule that states that when your speed changes your movement also changes; however, we have this from the "Movement and Position" section:

On your turn, you can move a distance up to your speed...

The distance you can move on your turn literally is your speed and so if your speed changed, the maximum distance you could move would also have to change.

If ray of frost were cast on you after moving 10 feet then you would now have 20 speed, and thus the maximum distance you could move would be 20. Therefore, you have 10 feet of movement left.

If longstrider were cast on you after moving 10 feet then you would now have 40 speed, and thus the maximum distance you could move would be 40. Therefore, you have 30 feet of movement left.

If you were grappling somebody your speed would be 15, and if you moved 15 feet and then released the grapple your speed would become 30. Thus the maximum distance you could move on that turn is 30, and you would have 15 feet of movement left.

Instead of thinking about your movement draining the amount of feet you have left, think of it as increasing the amount of feet you have spent, and compare the amount spent to your current speed. Then if your current speed still exceeds the amount of feet you have spent, you can continue moving, if the amount of feet you have spent equals (or is higher than) your current speed, you cannot move until that changes either by raising your current speed back above the amount of feet spent, or by using the Dash Action which allows you to compare your speed x2 (or x3 for double dash) to the amount of feet spent instead.

For example, if you move 25 feet with a speed of 30, you don't have 5 feet left as much as you have 25 feet spent. Then if you try to move further, your speed of 30 is still higher than your feet spent of 25, meaning you can continue. If ray of frost were to be cast on you after your initial 25 feet however, your current speed would be 20, making it less than the 25 feet spent, meaning you could not move. At this point you could take the dash action, allowing you to use twice your current speed in this "calculation" making for 40, which, being higher than 25 feet, would allow you to move for another 15 feet. Or you could instead use your action to cast longstrider on yourself to raise your speed back up to 30, meaning your current speed once again exceeds the amount of feet you have spent on that turn, thereby allowing you to move another 5 feet.