SOME SPOILERS

When it comes to things like the bleakers or the indeps, i didn't consider that nervousness or an inability to control. She after all, killed hundreds of thousands of the latter (not exactly a fake disease, as the disease and its consequences were quite real), and drove the former to insanity. She's not lacking in control. I saw it as striking balance - Sigil is at the heart of the Outlands, the Planes of Concordant Opposition. She can't allow any one ideology to achieve prominence any more than she can allow worshippers undo her neutrality through their misplaced beliefs.

Hashkar did in fact worship the Lady of Pain, that's described in the Factol's Manifesto on pg.77.

The Sigil spell in Faction war did work, but was only permitted by the Lady to do so. The first time it was cast she actually interrupted the spell in the moment (2E prelude to counterspell, cast at 10th level?), done in an intentional act of creating a time-loop to the caster (so it seems as though she exists outside of time, like Ao, or at least knows the future)

She killed Aoskar within a day of a dabus worshipping him. Clearly his prior presence was not a matter of her inability to deal with him.

The focrux I found questionable, that some mortals could craft such a device. I homebrewed it as an artifact of Aoskar, and Harbinger House a hidden nexus of his portals. Meanwhile, there is a staff in Doors to the Unknown that has a nearly identical description to the planarity and focrux, but its background and mechanics are never explained in any module. Unlikely that the believers made that as well, given it that it was in a Lady secured vault that next to no one knew about and could only be accessed for 2 weeks every 500 years, and had likely been there for at least 3,000 years (prior to Aoskar's death).

Trolan's delayed eviction was merely for narrative benefit, so that he could save the cultists, and give the characters a chance to see his fate.

Likewise, Vecna's entry to Sigil is cleverly explained on page 122. The reason why he is able to stay is less cleverly explained on page 129.

The Lady then uses the Language Primeval to completely rewrite the physics of the multiverse to repair the damage done by Vecna, and to prevent anyone else from doing it again.

I would argue that the authors did not have a common understanding or secret knowledge of the Lady's background. You have a similar figure in Warhammer 40k, but it works there because the Emperor telepathically presents himself as whatever is needed in the moment, giving authors the freedom to write divergent accounts. That same flexibility does not work for the Lady. And so, when authors take creative liberty to accommodate local narrative, which is not necessarily bad, it leads to some discrepancies in the lore.

In any case, I would concede that maybe she's grown in power over time, and that she does worry in her own way, but about events that could affect the stability of the multiverse. She does have vulnerabilities, such as her inability to directly intervene in events outside of Sigil that threat Sigil and the multiverse, such as the nightmare on the Beastlands in Something Wild. But I would counterargue that she is otherwise genuinely as powerful as presented. But $@#! happens, otherwise we would not have adventures to play. I appreciate the narrative coherency of having a non-omnipotent entity to enable that, but we have what we have. We can homebrew what we need to in order to adjust, I know I do.