The TGA image file format does support compression.
But whether UE4 supports the compressed TGA format I have not tested it.
TGA compression is lossless RLE (run length encoded). So it typically doesn’t offer much compression in size unless the image has large regions of the same pixel values.
PNG compression is lossless DEFLATE (similar to Zip). So it typically can compress complex images fairly well.
Both image formats are not relevant to what actually ends up in-game, as the bitmap image from the graphics file is converted for use in the engine.
There are some variations between the two image formats for support of pixel types and alpha channels.