Question begs questions..... What do you want the software to do? Ad probably as importantly, WHY?
I shoot digital for 'convenience', if I want to 'faff' I'd shoot film! Which was were the 'Digtal Darkroom' was a major breakthrough; doesn't do much that wasn't possible with chemicals, but it IS rather a lot less smelly! However.. Mantra was, and still is,'"Get it Clean in Camera".. get it as 'right' as possible before you press the shutter button, and less you need to 'put right' in post process,
Ironic phenomenon of widgetal, then is that all the 'convenience' it offers shooting direct to data, results in around five times the number of pictures, WHICH, if you didn't apply that CinC discipline to start with, beg ever 'more' post-process 'correction', and by a law of diminishing returns, the entire process rapidly becomes ever less 'convenient'.
'Best' employments of Post-Process, really are in the 'irregular' processes; things like 'Key-Stoning', correcting converging verticals, which following CinC you would need a tilt-shift perspective control lens for, you probably don't have, because they are expensive, fiddly and not needed 'that' often. Panorama Stitching; which similarly mimicks an UWA lens you probably don't have in the bag; or in exposure stacking, where contrast range of scene is just wider than you can capture with available dynamic range; These sort of things aren't so much error-corrections, used to put right stuff you got 'wrong' trying for CinC, but equipment 'patches', over-driving your 'gear' into the margins where it's really just not the right gear for the gig; to wit the suggestion is that Post-Process is probably not the 'best' solution, and if you are having to use 'post' to effect these patches regularly, it's saying 'really' you don't have the gear to do what you want to... Beyond that, you get into the 'creative' potential of the Digital Dark-room; multiple image montages, curious image manipulations like bass relief, solarisation, or 'cross-processing'. Here in lies a world beyond what you can do in camera, BUT, where, like using it for equipment-patches, best results start at the inception before you press the shutter button, shooting expressly to post process, and capture the elements you need to make the image you imagine.
The habitual use of post-process, 'as a matter of course', often suggested if not forced by RAW, to play with sliders and adjust out-put curves, before creating a display Jpeg, is something of an anathema in that irony, throwing away a large chunk of that digital convenience at source, and loading up the work-load in post, to do so much 'more', which should be unnecessary, IF you put that little extra in up front to get it CinC...
Which doesn't help answer your question very much, but suggest you ask why you ask it, and whether the answer to that would suggest a different question....
Photo-Shop is the incumbent 'Standard', and if you don't know what you are doing the one you are most likely to find tutorials or articles to help you learn, and which offers most features and effects any software does. In that respect, Photo-Shop 'Rivals', which may be as or even more powerful, and likely 'cheaper' are also a mine field where if you don't know why you want them, and don't know what you are doing, you are at the bottom of an even steeper learning curve, without any-one at the top able to chuck a rope down to give you a leg up.
Cheaper 'consumer' software usually doesn't have the versatility of PS, and instead offers a lot of 'one-touch' automated process 'effect filters', which can give you quick and easy results, but as a 'standardized' manipulation, aren't particularly 'creative' or necessarily the most suitable for your subject, and don't give you the control or encourage you learn how to effect that control to perform more intricate manipulations that may be more appropriate or creative.
Which brings us back to Photo-Shop, and suggestion, it IS probably the 'best choice', and if you can't afford it? Well, back to the top and questioning your question, DO you really 'need' it?
Which suggests I'm something of a PS propagandist, but I assure you I am not. I have a very love-hate relationship with that particular software! My favored pixels pushing program is a rather ancient edition of one called MicrografX, which is little more than a suped up version of MS-Paint, in many ways, but designed for a conventional Dark-Room Jockey like me in the early days, offered a lot of dark-room diddling in a way that was intuitive to get to grips with.. pitty it doesn't 'work' on 64-bit operating systems, or have 'large file' handling so crashes given anything much bigger than 80Mb to handle! So I have it on a 'dedicated' XP system I run my film scanner on, for 'occasional' use when PS is PSing me off! I have various versions of PS, the earliest dating back to the last century, when I was rather underwhelmed by it; but it was 'cheap'.
Which MAY beg suggestion to your dilemma; I do not use PS-Clown,I refuse to subscribe to subscription software. I don't have subscription TV, I'll be damned if I'll have subscription packages on my PC. So I still run PS6, and on another computer PS5. Full licences versions of these are available pretty cheaply second hand, and even more are available even more cheaply from more questionable sources. To wt, you can have Photo-Shop, and not have to pay the subscription, or pay an awful lot of money for it, and it could be as or cheaper than 'rivals' if you go-retro.....
Which may be a slightly more helpful answer to your question, BUT, still begs you question why you asked it and what you hope to do 'in post', and whether you'd be better putting the extra time and effort i upfront to get t CinC or auditing your gadget bag, as first course.