Yup, strengthening the back muscles is the most important part. I got rid of my lower back pain by sitting like this for half an hour (sometimes more) after I wake up: https://lowbackpainprogram.com/wp-content/uploads/2018/09/how-to-sit-to-relieve-back-pain.jpg
At the start it's a bit hard before the necessary muscles toughen up, but after a couple of days it's no problem at all and that sitting pose is quite enjoyable. Thats the only lower back strengthening I do daily and for the past six months I feel the best I felt since I injured my lower back so I highly recommend it.
Why would you shower a cat? They are pretty good at cleaning themselves