Dude, those are perfect homages
I know it was the idea, but the movie versions didn't seem so "poorly" done as these Modern versions were, for example -
1.
It's "shaky stick" because that's how the original model behaved in RoTJ. - Nope, just watched RoTJ, it's very stable and pivots mechanically like a ball joint. The one in the Mandalorian is definitely a shaky dude holding a stick.
2. The "human in a box" was actually different droid to the "shaky stick" - The GNK carrier - referred to as power droid, gonk droid or ammunition droid (Battlefield games). It appeared in the very first film, remained with us ever since and
it looks that way because it's exactly how it was in Ep 4. - It looks the same, but the actors inside doing the walking did a much better job in Ep4, 5 & 6 of not appearing exactly like a Human in a Box (subjective TBF).
3. The "non roasted creature" - Kowakian Monkey-Lizard - Jabba The Hutt's pet of choice - "cheaply made" as you noticed -
I'm sure was actually the original Henson puppet from RoTJ. - It looked so cheap in bright sunlight. Maybe the "movie" version had better lighting (it was dark in Jabba's during Ep6) which hid just how poor it was, if it is indeed the exact same model but I don't think it was, I think it's a newly made model that just looks low quality because the close-ups in Ep6, even when dark, still looked to be a much higher quality of model.
TBF most of it is subjective but I felt the puppeteering, compared to the SW movies, was sub-par.