Going to try and respond to this after forever
So what exactly am I missing in the Squigly matchup?
Everyone says it's a free win for Parasoul?!
IMO, I wouldn't say its free. I do kind of think its Parasoul advantage, but at best it would be only slight, and is very even for the most part I think.
Even if I agree with what you say though, I'll try to throw some advice at the things you point out and see if it makes any sense or helps.
1. Tearshots and Tosses are grossly inefficient, because they don't allow you to keep Squigly from getting charge, and after that it's pretty much impossible to do either of them
2. In the same vein, things like TK Toss j.LP are not much of a threat to Squigly, as she doesn't have to move in.
3. Para j.LP and j.LK get beaten by Squigly j.LK rather fucking consistently
4. Squigly j.HP is rather difficult to handle, as Para mobility is bad enough to not just get in vs predictable jumps, her hitbox is tall and PS will never get a combo out of swatting it, while Squigly gets full converts out of j.HP land SBO
5. Squigly has a really easy time gaining height and thus both get into a position where most of Paras air normals don't hit + Pillar deadspace becomes a thing
6. Threat of Sing Daisy forces you to jump a lot, which is something you don't want to do, ESPECIALLY not if you can't at least control the space in front of you with jump normals / toss business (you can't, cus then you eat Sing SBO)
7. c.MP is really easy for Squigly to avoid due to the speed at which she moves vertically
8. Her c.MK grossly outranges every other useful button Parasoul got (and actually hits at spots where PS c.MP won't, due to PS moving backwards during its animation)
9. As you're not really able to keep her from getting charge nor force her to use it without getting hit in the process, she'll usually have P stance charged = Much better defence than you got with charged DP and Doublejump
10. Divekick is very difficult to avoid due to bad backwards movement (backdash sometimes works to dodge it, but backdash into button rarely leads to anything)
tbc
1. Shots shouldn't be used, imo, to really really keep squiggly completely locked down form charging, since in all likeliness she'll have an assist to cover her while she walks back to get charge anyways. Squiggly getting charge isn't the end of the world, and you *can* still use tear shots in certain spots against squiggly when she has charge, its just best to avoid them in obvious times like if you were trying to zone her. Ideally, I think of using Napalm shots as a part of continued pressure like from blockstrings, something to use as a way to get in, is what you should be using it for, rather than the defensive use like when you use them against filia/bella.
2. I can't comment specifically about the theory, but I have found TK toss jLP useful before though I can't describe it perfectly or know why. *I think* I used it as a meaty for when I suspect Squiggly to approach, since it covers ground and air approach decently well. One example is after they use a singxSBO on you but they whiff it and start to get in close on you for pressure/mixup, though parasoul already has plenty of tools in that scenario already. Its not an amazing tool to use since it doesn't easily beat out squiggly jHP, I wouldn't put it as useless on the defensive side.
3. The interaction of those buttons is basically just momentum. If you are using too much jLP/jLK for your approach, they can easily time an air-to-air to beat you. However, there are times you can be preemptive or even react to their whiff jLK and beat them out (anytime I've whiff punished jLK, it was close by, fwiw).
4. Not gonna lie, I can't even explain my own thinking about how I play against this. Need to play another set against a good squiggly since its been a while, but from what I recall it was just a bunch of whiff punishing in various ways, and yeah most of them didn't lead to full conversion. Can't help much here atm since I don't remember exactly.
5. Basically related to 3 and 4. If you can't keep Squiggly in check on those, she's going to dominate the air coverage, and will have free reign to jump in, from which she can get all the divekick pressure she wants. Once you start combating her there though, she'll run out of options and she'll have to work harder to get in divekick timing/range.
6. Sing Daisy isn't too bad since if she's holding stance and has charge ready, you can easily walk forward on her and you can general react in the air to Daisy even from sing. Just walk forward to close in the distance, and jump when you are in close range to her so her daisy will whiff (since you can react in the air with toss) but still block in case they go for sbo. Worst case scenario, you are blocking and they wasted sing+meter if they were obviously holding charge waiting for you to do something stupid. Just be more patient and don't leave yourself open and be ready for the sing and you should be able to deal with it.
7. This is true though there are some other Parasoul AAs that you can use instead, such as jMP and you noted yourself cHP can work too. If squiggly is on the ground, where you want her to be of course, then yeah cMP still works great (which goes into the next point I guess).
8. I'll be honest, yeah her cMK is a fantastic button, but I've not lost yet using cMP against that button? cMP moving her hitbox back makes it much easier to use it as a whiff punish tool including squiggly cMK. In either case, anytime a squiggly would go for a run up cMK in neutral, thats usually free napalm shot or jump in jHP (both of which are technicaly reactable with super though I've not seen a squiggly do that yet), even ignoring cMP. Not sure what scenario here where cMK is beating out everything you can do.
9. One comment I'll make about squiggly charge is that I like to use plentiful use of Egret Charge nowadays. Technically, not at all distances/times will it catch her, but a lot of times it actually can catch squiggly if she tries to react with SingxxSBO (no help against daisy though I've not been daisy'd out of Bike). Basically, throwing out bikes when you've established a whiff punish game against her air approaches is good at making her second guess trying to fish out with SingxxSBO. And doing that goes a long way of taking off some of her pressure and allows you to close some distance in.
10. I've been okay with Backdash sLP and sometimes sMP as a whiff punish against Divekick, though napalm shot also works too and even is good if they block it. As someone who backdashes waaaaaaaaaaaay too much, I've felt fine with backdashing against squiggly.