If you have the post-2022 HD560S, then I think you’re already ahead of the game. And probably have one of the better kept secrets in the lower-end market. There are some areas where I think the HD560S could still be improved though. So let’s talk a little about some of those. 
The frequency response, while relatively neutral, is a little uneven imo. The post-2022 version is a step up though in response from the pre-2022 version imo, based on the available graphs.
Like most other open dynamic headphones, the HD560S is rolled off in the sub-bass. That is one of the physical limitations of open dynamic designs, regrettably… There is some good news though. The post-2022 HD560S is probably a little better extended there than the pre-2022 version. And it is also better extened in the sub-bass than some of its more expensive brethren, like the HD600 and even the HD650. It is probably also lower in distortion in the sub-bass frequencies than these 6 series headphones, which means that more sub-bass can be added with some EQ. So if you need deeper sub-bass, the post-2022 HD560S may have a few advantages over some other classic dynamic headphones. (There are still limits though to how much boosting you can do in the sub-bass on any open dynamic headphone. And the HD560S is no exception.)
It is also a bit strident in the upper mids/low treble. Which gives the HD560S a somewhat more aggressive, in-your-face character. There is some good news here as well. Because the post-2022 version is better balanced there than the pre-2022 version imo. And it’s fairly easy to dial that stridency back a bit more with EQ.
The HD560S has a resonance at around 4 kHz. And it also has a peak in its distortion at the same frequency. This is part of the stridency I mentioned above, but it will also impart some sibilance as well… which probably sounds like a bad thing. But there’s a silver lining there as well. Because, by EQ-ing down the resonance, you’ll also reduce the audibility of the distortion in that range… which is a good thing. Better timbre plus also lower distortion.
The distortion is probably about average though on the HD560S for a lower cost headphone. And there are other headphones that have lower disortion across the board than the HD560S. So there is still some room for improvement there.
The treble on the HD560S is also a bit uneven. And a bit dark, and also sibilant in a couple spots. Isolating and correcting this is a bit more challenging, but it can be done with some good headphone frequency modeling imo. We are slightly impaired there by the fact that there are no good 5128 measurements currently available for the post-2022 version of the HD560S (that I’m aware of). All of the 5128 measurements that I’ve seen so far appear to be for the pre-2022 version. There are some workarounds for this. But it’s a disadvantage not to have some actual raw measurements done by some reliable graphers, like the folks here.
If you are doing critical listening, good measurements add value to your headphones or other transducers imo. Because they make it easier to compare the response of your headphones to other good products, with maybe an even better or more neutral response.
You might wonder why the HD560S has better extension and distortion in the sub-bass than some more expensive or well-known and regarded open dynamic models. Part of the answer to that is it uses a new driver design, which is part of the SYS line. The other answer may have something to do with the HD560S’s cups and baffles which are a bit more compact and enclosed than the 6 or 8 series Sennheisers.
While this may make it possible for the headphone to dig a bit deeper into the lower registers, the more compact/enclosed design also has some potential comfort and sound quality tradeoffs, like potentially worse breathability, a less open sound, and not as good pinna interaction. Headphones with larger and more open cups will give you a more open sound with better pinna interaction. And lower acoustic impedance, which may provide a little better consistency to the sound quality. And they may also breath and dissipate heat a little better.
The angled drivers and one-sided cable on the HD560S also have pros and cons imo. The angled drivers may contribute to the illusion of space a bit. But they also make it more difficult to test the symmetry of the headphone’s drivers by reversing the earcups from left to right. Single-sided cables that attach to only one earcup may be easier to manufacture and replace. And some people may prefer fewer wires in their way in a studio. On some headphones though, they may also result in a weight imbalance and contribute to symmetry issues. I haven’t noticed much of that on the HD560S. But this is a “convenience” feature (mostly for the headphone mfrs imo) that you’re more likely to find on lower-cost headphones than on the higher-end models. Probably for good reasons.
These are all areas where there’s some potential room for improvement in the HD560S’s performance imo.