"Old" vs new Shimano 9-speed compatibility?
Yes, the rear derailleurs are completely acceptable, the cable pull ratio did not change. You will not get any new features of SHADOW PLUS you get in new generations of XT.
A year ago I still saw XT M772 Shadow on offer, but it seems to be unavailable now. Deore M592 Shadow seems to be still available here and there. You might be interested in that instead of the lower Acera or Alivio lines.
A new derailleur might function better than a used 20-years old one, but you certainly won't get such tight tolerances, such good materials and such high-quality pivots in the low-end lines. Be prepared they may not remain in such a good condition, the old one remained to be, for such a long time. The pivots might become loose, for example.