I detest the stale bot :-)
And I really think it only is a disservice to the project, 99% times I see it used. If the code has a genuine, real defect, it will not "go away" magically just because nobody complained again, or the authors didn't have time to look on it.
See, the issue is there. Don't have time? Ok leave the issue open, it acts as a documentation about, well, that there is an unsolved issue.
I really hate when googling about some problem and then finding a promising bug tracker conversation that then... got comments closed because of old age. That's literally swiping the problem under the rug.
Now regarding burnout and burden of OSS maintainers, I might lack a bit of empathy here, but I just don't get it. Really the license text says it all: THIS PROJECT IS OFFERED AS-IS. Most if not all OSS licenses have a phrase like this. Just quote those words 100 times if it's needed. My mental health as an OSS maintainer is very well and I cannot see it being changed by some, even lots, of demanding users at any point. Every time someone takes my code and uses it, there is an implicit conversation where I go "hey, here you are take this work for free, I'm lending it to you AS-IS, do whatever you want with it!". Absolutely at no point in time I feel pressure about defects in the code, after having this imaginary conversation.
I guess we need more spreading of the notion of "not giving a sh*t" so the idea gets extended to more and more OSS maintainers, helping them have a happy life not encumbered by the work they decided to release by sheer goodness. EDIT: with this last phrase I mean that one should have the mentality of contributing up to, and not more, what one is able to do within their own limits. The "not caring" I mention is for after reaching this limit: it will help not pushing through the burnout line, and thus as a result being happier in the long term.