I never explored joysticks for playing simulators on PC. Can some kind of joystick simulate aerodynamic lock during spin? You do hands off control stick and it stays there, won’t center as usual. I understand that force feedback is often included in such products, but can force feedback override auto centering?
Yes there are PC joysticks that can remain in an off center position: the active feedback joysticks, without the force feedback switched on. The stick feels pretty light in that situation and kind of remains where you put it, almost like a helicopter cyclic stick with the trim button released.
When switched on, the force feedback can act like a passive spring and accepts some input parameters for varying the feel. The neutral position can be varied, the return position of the spring. All pretty course, not bad for the money, although the stepper motor produces grainy feedback forces.
I think it's more of a question about the simulator software than the joystick. For example Flight Simulator 2004 did have force feedback modeled into it, but I don't recall it being very sophisticated. I do not know the current status of "consumer grade" sim software, but I'm highly doubtful that they would be able to mimick actual feel of stick forces in a very natural way. Doing it would require quite a lot of computation.
FS2004 did emulate the affect of speed on control forces, but it was pretty crude.
Such effects can only be produced by so called 'force feedback' (FFB) devices. They exist, but few of them, if any (in the consumer market) produce satisfactory results.
Good force feedback simply cannot be done cheaply, and this restricts the market to niche enthusiasts and professionals. It is relatively easy to produce 'effects' such as vibration and impulses, and most consumer FFBs can do it. But to simulate the whole range of forces reqire a specialised drive and very solid construction.
In addition (and perhaps because of the small niche market of such devices), none of the common game simulators even attempt to simulate control forces reasonably. Tellingly, even the Windows interface (API) to drive FFB hasn't been updated for some 15-20 years (it even retarded a bit).
But all is not that bad. While I'm still not aware of any FFB stick/joystick controller that can do a satisfactory job, there are at least FFB yokes (such as this one) that can potentially deliver a relevant experience in GA aviation. They are not cheap by gaming standards ($1500+), but very cheap by aviation standards. To overcome software limitations, they typically extract flight data from the games and run their own force simulation, which requires some fiddling with set-up.
The car racing game industry is in a better position: the number of enthusiasts is larger, and an FFB steering wheel is a simpler device (being a single degree of freedom and lower force). There are quite a few racing FFB steering wheels on the market that can be considered decent, but even they are fairly expensive (~$1000).