Compression on the PS1 is not going to be too radical, though it is powerful enough to get us into real compressions (compared to SNES stuff where it was a bit simpler). https://ece.uwaterloo.ca/~ece611/LempelZiv.pdf
if you wanted an overview on the types available. It is curious that some things work and others might not.
To that end you might want to grab the texture in the ROM (presumably a nice name, directory name, corruption, file swapping effort or the like telling you what it is) and grab the texture from RAM when it is being used.
You can then compare the two and see what was changed for it.
You don't even necessarily have to make a tool to compress it again afterwards (that would be a harder task, though you might be able to adapt an existing one as most things just vary LZ compression in the location/amount split, window size and values used for flags) -- most LZ compression has a "nothing compressed in this section" flag however many bytes apart for that implementation. Make every section have this flag (trivial to do really) and then even if the game tries to decompress it then all it will in essence be doing is copying every section in to make the whole file.