How does the updated Centaur work with an effect of 'gain a climbing speed equal to your current speed'?

Question

I am building a College of Satire Bard from the Unearthed Arcana: Kits of Old mentioned here. I found the PDF on wizards.com.

The two rules elements are quoted below. There are three similar questions, but they don't seem to address my specific question:

• What is a Centaur Thief's climbing speed?
  This suggests the Thief would negate Equine Bond, but with Tumbling Fool you just gain a Climbing speed equal to your current speed. I don't think that is the same effect?
• Is there a functional difference between having a listed climb speed and being able to climb at full walking speed?
  This also deals with the same effect as the first question, but also dives into how items interact.
• How does the Athlete feat affect the Centaur playable race?
  Finally, this also deals with ignoring extra movement.

The Question:

What is your climbing speed and what restrictions do you have with Equine Build and Tumbling Fool?
Or more precisely, does the ability of "climbing speed equal to your current speed" also work the same as "no longer costs you extra" effects?

The Rules text:

The updated Centaur on page 9 of Mordenkainen Presents: Monsters of the Multiverse has an ability called Equine Build:

You count as one size larger when determining your carrying capacity and the weight you can push or drag.
In addition, any climb that requires hands and feet is especially difficult for you because of your equine legs. When you make such a climb, each foot of movement costs you 4 extra feet instead of the normal 1 extra foot.

The 3rd level ability Tumbling Fool has these rules:

At 3rd level, you master a variety of acrobatic techniques that allow you to evade danger. As a bonus action, you can tumble. When you tumble, you gain the following benefits for the rest of your turn:
• You gain the benefits of taking the Dash and Disengage actions.
• You gain a climbing speed equal to your current speed.
• You take half damage from falling.

Answer 1

Rules as written, Tumbling Fool completely undoes the effects of Equine Build, so you climb at the same speed you travel by foot (or hoof I guess). Equine Build is modifying a general rule for how you use your normal (non-climbing) speed to climb when you don't have a climbing speed; Tumbling Fool gives you a climbing speed, so the rules for climbing without a climbing speed no longer apply, and therefore neither does Equine Build.

It would be entirely reasonable for a DM to say "Nope, that's complete nonsense" and house rule things (e.g. they might split the difference and have you effectively have a climbing speed of half or a third or a quarter of your speed, any of which would still be better than one fifth of your speed), but it's a very clear interaction as written; when they don't have a climbing speed, centaurs are bad at climbing, but if they gain a climbing speed by any means, they're as good as anyone else with that climbing speed.