Not sure if I understand everything you wrote here correctly, but to answer your points once more:
1) The Pershing wasn't able to pump more AT DPS before or during the heavy meta and this hasn't changed at all up to now. Literally the only thing that has changed since the 2019 AoE nerf is that all heavies (except the KT and KV-2) were made less effective in sniping full-health models while still spreading massive HP damage across all members of a squad. And here the status quo also remained largely unchanged; both the IS-2 and Pershing deal significantly more AI DPS per shot than the Tiger, which in part makes up for the slightly worse AoE with its higher rate of fire. If anything the Tiger was even hit harder than the other heavies by the AoE adjustments, since it lost quite a bit more AI relative to the pre-patch version (especially if you consider the loss of the vet2 scatter reduction).
2) Again, CA doesn't promote blobbing in any form since you can literally have one engie squad trailing behind at half a screen distance to get the desired buff for your tank. Sure a giant deathball around your tanks will enjoy the same benefits, but that doesn't mean you can't get the most out of CA without blobbing.
3) Again, the Tiger winning an isolated 1v1 brawl against the Pershing (and IS-2 for that matter) is how things have been for years and isn't a new development nor was it different during the heavy meta. I'm personally not against giving the Pershing slightly more armor or reducing the price a bit to better match the performance difference in this particular matchup, but that's not up to me.
4) This is basically an amalgamation of the above, so just to reiterate: no the Pershing doesn't have worse DPS against infantry and, yes, it does lose against a Tiger in a head-to-head duel. Part of this is already getting addressed in the beta as it has been said numerous times before, but some degree of performance difference will remain simply because both units have different factional units to complement their respective weaknesses.
There's no doubt that a bit of further tweaking would surely benefit the Pershing, but the tank itself is nowhere near as useless or underpowered as portrayed here. I remember a similar discussion revolving around how absurdly UP the Tiger is compared to other heavies after the 2019 patch hit... funny to see how the tables have turned so quickly.
I agree with everything said.
However, "CA doesn't promote blobbing". If you really want to get your worth (Now 110 muni), you really need to have multiple units next to the Pershing. I quite often play Heavy Cav in 3v3s and if I can barely fit another tank with the Pershing (usually Jackson). Howi, AA, mainline squads (+ ranger), 2x RE, maybe AT gun and the Pershing. And it would be really stupid, for a lack of better word, to use a 110 muni ability to buff ROF and range of one tank where the extra range won't be utilized because of sight constraints. And for the extra ROF. You really gonna waste 100+ muni just to shoot a second or so faster?
So if you want to get your money's worth, you need to have a couple of squads around it so they too get the bonus, which is just asking for an offmap/indirect. Eg. I consider the skillshot quite useless even though I successfully killed a fresh snared Tiger on Angrymundy last game through 3 or so buildings on max range. I also consider CA to be quite a hogwash even though I've also successfully used it a couple of times in past few games. I will say that CA is good for a hail Mary push. That it most definitely is. On maps that are wide enough ofc. Whiteball and the such. Using CA on maps like ettelbruck or angrymundy is just plain idiotic as there are plenty of sightblockers, buildings, pathblockers, etc.
The Pershing is not as bad as people make it out to be, but in 3v3+ games, it's quite useless. Sooner or later Tigers, JP4s, KTs hit the field and without rocket arty to at least displace the supporting infantry around those mammoths, you won't stand a chance with a Jackson + Pershing + mainlines against 3x Obers + KT + JP4 + stuka or werfer + Tiger + Panther + PZgrens or some elite doctrinals.
Furthermore, theekvn pretty much tested out the AI, where Pershing should have a bigger advantage over the Tiger, and shown that it doesn't even have an AI advantage. Sure the test samples are low but the results are consistent. About the bigger penetration on Pershing. It's going against stock Panther (260), JP4 (230), OKW P4 (234) and maybe doctrinal Tiger (300), Elefant, Jagd (400+). Tiger goes against Sherman (160), Jackson (does it even have armour?), and maybe doctrinal Pershing (270) or E8 (215) or some dozers (200+). All in all, the 20 less penetration on Tiger is quite fine. Other factions like the brits have some beefier tanks but that's where the Panther comes to play.
The double standard is not really a myth here. While I understand that buffing Pershing (mostly a 2v2+ unit) could have adverse effects on 1v1, I do not understand why buffing armour back to 300 and slightly buffing frontal MGs is out of question? The Pershing is not anywhere close to being OP. Even in the standard army composition. Even with a Jackson backing it up.
Edit: If I'd have to rate myself in COH2 I'd be "3.6". Not great, not terrible. Not as retarded but sometimes retarded. So when I keep winning using a braindead tactics, you know the balance is skewed.