^ +1 if the OP interest warrants the hike in budget and learning-curve?
Spending the dosh on a good lens vs a ‘good enough’ body is generally accepted a better choice than vice-versa. I would echo that, having ‘splashed out’ £100 on a budget zoom lens when I began getting into digital DSLR. The images were so dark and mushy that I wasn’t happy with one single frame. I sold the lens at a loss not long afterwards!
400mm telephoto is considered a decent minimum reach for birding. You’d still need to be fairly close to the feeder to fill a frame with the bird. 400mm lens on a full-frame camera body would be IIRC roughly equivalent equivalent to 8x optical magnification with binoculars?
You’d ideally be 20ft or closer from the feeder. 15ft would be better. A popup bird hide/blind could be a good investment.
Also a sturdy tripod with a pan-head. I paid about £100 for a trekking tripod but you could get a decent used tripod for £50? A pan-head is a good compromise for long lenses. A ball-head best avoided for same. A gimbal head is probably best for bird photography but there are typically much more expensive.
Camera body? Plenty to choose from but assuming buying used just be sure to but one with a relatively low shutter-count rather than high as shutter rebuilds are prohibitively costly for budget DSLR. Low to mid-end models looking at 50k-150k shutter actuations life span, so be looking for half that or less on a used model.
On a mirrorless system you’d be typically looking at a longer life span.
Only worry about service life if buying an older used body. Or buy from a reputable used dealer with some kind of assurance.