manipulate - Animate bookmarks which do not set values for all parameters

I have a Manipulate with bookmarks which do not set the value of all parameters; only some. A MWE is:

Manipulate[{x, y}, {x, 0, 1}, {y, 0, 1}, 
  Bookmarks -> {"beginning" :> {x = 0}, "halfway" :> {x = 0.5}, "end" :> {x = 1}}]

The problem comes when I click on "Animate bookmarks". Ideally, I would like the animation of bookmarks to keep the current value of parameter y (i.e. the unset parameter). However, this is what I get in Mathematica 11.3:

My naive (and unsuccessful) attempt to solve this was:

Manipulate[{x, y}, {x, 0, 1}, {y, 0, 1}, 

  Bookmarks -> {"beginning" :> {x = 0, y = y},"halfway" :> {x = 0.5, y = y}, "end" :> {x = 1, y = y}}]

I would really appreciate any help on this. If it is not possible to solve this problem, do you know if there is any way of disabling the "Animate bookmarks" feature?

Thank you so much for reading up to here, Best, Luis

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