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I need to slide (right or left) a whole layer (I mean the layer in the timeline) but I can only expand or shrink it, not move it as a block left or right (like we can do it in after effects when grabbing the layer with the left mouse button and sliding it).

Move cursor over one of the layer's frames, left-click and hold. Now, drag right (or drag left if there is any room).

And notice that there is now a lock command (RMB on layer) to prevent the layer from being accidentally shifted.

Oh thank you I couldn't have found otherwise for anim layers ^^
(I lost so much time today because of this ><)