I guarantee engineers love working for you because of this. If you look at Maslow's hierarchy of needs you are filling that esteem portion that is really lacking for a lot of software engineering teams in the wild.
A lot of it isn't a complex secret, it's really doing what you pointed out - make people feel appreciated, listened to, and actually part of the company as a whole as opposed to just a resource. This can be as simple as being more transparent as to why a feature has been requested, even if it's counter-intuitive to reason, or giving context as to where the roadmap is heading so that they're aware on why they're working on something.
As an engineer I've always found that knowing why, knowing that there is a real customer out there who really wants what I'm making is very motivating.
So often people just come to me because their boss told them to go get engineering to make this thing. They don't know why, and sadly, their boss doesn't know why either as it was just passed to them from an executive mandate. And there is lots of pressure to get to done ASAP!
I believe this is why some of the best Product Owners I've worked with have some understanding of the technical side so that they can push back at the point of feature request rather than accept everything to please business/the client and lay it at the feet of engineers a few weeks down the line.
For this reason, I think the engineering manager/technical product owner type of role should start becoming a bit more common especially in startups, where I've seen first hand, POs brought in who subsequently drive products into the ground that were initially engineering led (and which raised the investment in the first place).
POs in my recent experience could benefit from listening more to their developers, who often know the domain much better than they do. (Or perhaps the wrong people are becoming POs)
I've stopped giving feedback and I'm nearly at a point where I've stopped being interested. It frees up my mind and motivates me to work on my own projects on nights and weekends so I can actually have a say.
This is often how waterfall projects are/were run in large companies historically but now companies want agile everywhere but they don't implement the right processes to facilitate it. You end up with behind closed door decisions, promises made by PO that it will be done in the next sprint, and at no point has anyone with either the courage or technical know-how stepped in to point out that it's not feasible.
This is true but I find if I can explain why the feedback was overlooked, that can help diminish the negative feeling. It hasn't happened often in my experience but sometimes when it has, if the idea is feasible and won't detract too much from the critical path, I would push the business team a bit harder to allow it so as to avoid the constant ignoring feeling that can happen.
Unsurprisingly, the former tends to get things out on time to huge success, and the latter tends to be late, and it barely scrapes across the finish line.
I haven't lived through a burnout yet, but I can relate to being stuck and unhirable, where your only background is in programming. No one will touch you for work in a different field because they figure you'll flee for a more lucrative dev role. No one will touch you for anything related to software, because they figure something must be wrong with you if you have the slightest gap in related employment. Devs are in such high demand, anyone good can find another job immediately, they'd say. Now you're in a self-perpetuating rut, and if you complain about it in the wrong community (not HN of course!), you just get told you must suck. It's completely demoralizing.
Went through that after graduating during the "Great Recession" and failing to find a dev position within six months of graduating. Ultimately, I clawed my way up (with a lot of help) after years of depression and suicidal ideation.
You may be headed away from programming, not back into like I was, but I really want you to take away the kind of encouragement online that I never received. Best of luck.
I often found that features would be requested from product owners/business and developers would implement it no questions asked but at lunch time, developers would rant about the requested feature's value. When asked if it should be brought to the PO's attention, I often saw the attitude of it not being their problem, they're getting paid either way (whether that's a company culture issue, general developer apathy, or burnt by past experience of questioning management is a different question). I think product-engineers feel a bit more invested in the product and have the soft-skills to influence or provide feedback in a manner conducive to business listening.
In my teams, I try to foster this type of communication and I've noticed a lot more developers opening up and providing valuable product-orientated feedback which often has an upward positive spiral of them feeling more appreciated and speaking more. Naturally a lot of engineers still want to just code and go home but team culture can really highlight and encourage engineers who may not be confident to speak up initially.
Ironically, as someone with more engineering experience on paper, it's been tricky to find a job directly as any form of product or engineer manager, I always had to go in as an engineer then be promoted after a year or so which isn't always ideal (or referred via a friend). I feel Product and Technical skills are still often considered mutually exclusive a lot of the time but I think that's inertia from when technical skills were still considered a cost to the business.