The stain IS uneven and that is because the underlying softwood was stained using dark pigmented stains made to be almost a paint in pigment particle size and intensity. They may have even thinned out some oil based paint to do this job. In some areas they really gobbed it on to hide something underneath the stain. Just like deck stains come in clear grades all the way to fully pigmented almost paint grade stains for older deckwood in poor condition, so do cheap pro level interior stains come in various pigment grades. These stains are made to even up different low grade wood species used in house trim. It appears the softwood paneling is a non stain grade plywood in the center panels and the surrounding trim and boards are likely a different species and do not color match when fully stripped. Poplar is a low cost white wood used for interior house trim but now a bunch of cheap tropical species are imported for just this pupose. I would avoid stripping to bare wood with sanding as the results may also not appeal to your eye and it will require a ton of time and sanpaper to strip this paneling to bare wood.
You can try sanding some of the heaviest areas of pigmented stain off the wood to try to even things up but realize that these heavily pigmented stains have probably penetrated deeply into some areas of the plywood paneling and left other areas only lightly pigmented. In other words they were trying to hide something (wood defects) and made things worse to your eye. A lot of paint grade sofwood trim is turned into stain grade trim by applying heavily pigmented stains at a thick coverage. Some people notice and many others do not so it keeps happening to save money as real stain grade interior wood trim is really expensive compared to cheap poplar white wood trim.
My only advice is to find an out of the way spot with several different problem areas, strip some paint off with sanding( 120- 150 grit to 220 grit final) and go back over it with foam or bristly brush applied lower pigmented stains to try to faux finish the problem areas. You may need two or three different colored pigemented oil based stains to get a result you like. Final finish with a semi gloss or matt varnish to even up the gloss. This is the kind of job you will be really good at when you are finished but not when you just start out. So work your way into the highest visibility areas last. Good luck