First of all: TPicture, by itself, does not have an alpha channel, it's not even a graphic format... It is just a helper class to allow the visual TImage component to handle different graphics formats.
The alpha channel is in the Bitmap property of TPicture (Image.Picture.Bitmap), but only if the bitmap has been setup for 32bits per pixel. And even then you will have a hard time manipulating the alpha channel in the LCL because TColor in the LCL does contain 4 bytes but the 4th byte is reserved for identification of system colors.
You should switch to another graphics library for manipulating alpha: BGRABitmap is a well-known candidate (the "A" stands for "alpha"), but it is an external library. If you want to use only built-in units you could take a TLazIntfImage and convert the Bitmap to a descendant of TFPCustomImage in which every pixel (Colors[x,y]) consists of four word-sized channels (.Red, .Green, .Blue, .Alpha).
Documentation about this is a bit scarce, maybe
https://wiki.freepascal.org/Developing_with_Graphics, or
https://wiki.freepascal.org/fcl-image.
I am attaching a little project in which a 24-bit Bitmap is loaded into a TImage with one distinct background color. And the pixels with this color are replaced by fully alpha-transparent pixels.