I’m talking about this
Except for the Colour Replacer tool (Tools > Colour Replacer), no.
There are many third party colour pickers available, I currently use JC Colour Picker in Windows.
It depends on what you call a “colour picker” and what you want to do with it.
In its simplest form, you access it through Format>Area, Area tab, Color button. When you hover the mouse over the palette samples, the colour name pop ups as a tool tip. There are two modes: with a shape selected (applies the change only to the shape), without a selected (defines the session default colour).
An alternate workflow avoids to reference the colour picker when creating the drawing. You first define a set of styles where you set a colour to the style with the colour picker. Afterwards, you only assign the style to the shape, transferring all the style attributes (not only the colour) to the shape.
I can’t find the icon you show in your question (it may depend on the computer graphical environment and you didn’t mention your OS, theme nor LO version). But usually this type of tool means “colour clone”. You click on an existing shape and its sets the current colour to the shape one.
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