How to change icon spacing in iPad?

Sorry, this is normal with iPadOS 15. There is nothing you can do to change this behavior.

Apple changed the way they display the icons to make sure that widgets are properly aligned with the rest of the icons, even when you are not using widgets.

As you have discovered, update to iPadOS15 introduced the ability to add Widgets to your Home Screens - some being added to your first Home Screen, by default, during the initial update to iPadOS 15.x.

Widgets placed on a Home Screen now individually occupy one or more elements of a 4x6 icon grid. Home Screens without Widgets retain the familiar 5x6 icon grid. With the grid accommodating fewer icons when Widgets are present, other App and Folder icons may be displaced to the next Home Screen - and this may have a ripple-effect where Home Screens icon grids are fully populated.

Removing Widgets from a Home Screen does not cause displaced icons to be restored to their prior locations. Re-arrangement must be done manually. This is perhaps a less onerous task than might initially appear, as Home Screen icons should still follow their original sequence (reading left-to-right / top-to-bottom). With multi-selection of App/Folder icons, it is possible to simultaneously move several icons if you wish.

The easiest way to restore icons to previous positions is to start with the first Home Screen - and remove any Widgets that you don’t require. 

Next, select the second Home Screen; icons displaced from the first Home Screen are likely to be at those starting at top-left. Drag App/Folder icons back to the first Home Screen - each likely to having been originally those appearing last in the sequence of the first Home Screen.

When you’re done, move onto the third Home Screen - moving icons back to the second Home Screen - and so on.

@LotusPilot

Thank you for correcting me and offering a solution. I didn't know it was possible.

@GM1440

I'm sorry to have told you it wasn't possible. Please follow LotusPilot's recommendations. And please mark LotusPilot's answer as Helpful so that others can benefit from LotusPilot's solution and see that my answer was incorrect.