You are losing image in rgba . Example:
ffmpeg -f lavfi -i color=color=black -loop 1 -i logo.png -filter_complex "\ [1:0] format=rgba,fade=in:st=0:d=3:alpha=1,fade=out:st=6:d=3:alpha=1 [ovr];\ [0:0][ovr] overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2\ " -t 10 -y out.gif
format=rgba - use RGB format with alpha for transparency
fade=in:st=0:d=3:alpha=1,fade=out:st=6:d=3:alpha=1 - disappears at start from 0 s for 3 s with alpha, disappears starting from 6 s for 3 s with alpha.
overlay=(main_w-overlay_w)/2:(main_h-overlay_h)/2 - overlay centered on the source

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