Best advice is place something that could act as a panel like a spare thick matress or anything similar to those acoustic panel and measure with REW. Check how much RT60 and ETC changes/improves, plus ny change in frequency response. Then decide if its worth installing them by DIY of buying them.
It is a small room, biggest problem will be in the bass department, because the bookshelfs are literally against the corner (pressure maxima location) , and no bass trap will help without stealing Half of your available space.
4” is thick but still that will only absorb from bottom mids to highs. The same effect could be achieved by rugged maths, carpet, furniture,etc. But since your room is quite empty, the panels could be a good idea to compensate the lack of absorbing surfaces.
I don’t think placing some panels and diffusers where you want could make any harm. Give it a try and I hope you like the change (most likely you will). If not, you could always go back. Just don’t expect drastic changes or will get disappointed by results.