You are still limited by your speed, but have other benefits
The rules for movement say
Your movement during encounter mode depends on the actions and other abilities you use. Whether you Stride, Step, Swim, or Climb, the maximum distance you can move is based on your Speed.
The boots do not say they remove the limit so they do not. The boots however do not only increase your jump distance. The core function of these boots is:
When you Activate the blast boots, you can High Jump or Long Jump, without the need to Stride first.
So you still get value out of them. Normally to long jump:
You Stride, then make a horizontal Leap (...) If you didn’t Stride at least 10 feet, or if you attempt to jump in a different direction than your Stride, you automatically fail your check.
With the boots, you don't need to waste 10 feet of your Speed first, you can directly jump, and because you do not need to stride, in any direction. The moderate version of the boots also adds this second capability:
When you Activate the moderate blast boots to High Jump, you can increase the vertical distance of your High Jump by up to 30 feet
This is within the movement of most characters. So unless you have a high movement or want to jump high, you should just buy the lesser version of the boots, which are considerably cheaper at 3 gp, compared to the 11 gp for moderate boots.