There are chapters related to this subject in any number of books. One that came to hand quickly this morning was "The Science of Musical Sound," by John R. Pierce, published in 1992 by Scientific American Books. It includes chapters on Architectural Acoustics and Sound Reproduction.
EDIT (half a day later): There are also many websites that understand these problem better than do those who play music (like most of us here): this is one site I just found: https://ehomerecordingstudio.com/acoustic-treatment/
Last year, my son finished building a complete recording studio (with acoustically isolated and controllable/tunable performance/recording space) on his property; new building entirely devoted to this function for his "hobby business," "Black Range Recording". I questioned him with reference to your request and he told me that the company GIK Acoustics had been very helpful to him.
He has been musical since he was 5 years old: https://www.n1m.com/josephvictor/about
After high school 40 years ago, he spent a year attending recording engineering school in Los Angeles (following the advice of a family friend, recording engineering "tonemaster" Stan Ricker).
To increase the reverb, get rid of the rug, and other sound absorbing items in the room, such as curtains, pillows, sofas, etc.
The drywall may be absorbing quite a bit of the sound. It is probably not practical to install hardwood walling.
You could opt for some old plate reverb units if you really want more reverb. You could also consider using a digital solution and add reverb with speakers.
Richard (above) has some good suggestions--furniture to break up the flat surfaces, and I use absorbent rugs on the floor and walls. Unless you have a high-ceiling space with surfaces that are not parallel, you shouldn't expect to get a very good reverb in your space. Instead you should ideally seek to mute the standing waves so that you get a nice resonance to which you add reverb digitally.
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