RJ has his chief observer of the Aes Sedai, Egwene, voice contempt for the strength=any character trait system quite early. Moghedien is one of the first Forsaken we spend any amount of time with, and she's far stronger than the majority of the channelers we meet, but she is shown to be anything but bold. Asmodean is shown to be cowardly too, yet he too is way stronger than most we meet.
The strength-boldness correlation simply does not exist.
What on earth are you talking about? Every single person you noted as "bold" is one of the absolute strongest channelers in the series. I'm not making any statement that there is a linear correlation between strength and boldness, just noting that in general the stronger OP characters are also bold and the weaker ones are generally less bold.
She is hiding her face from Alviarin because her Aes Sedai disguise looks like her actual self. It makes great sense to not reveal that to an underling greedy for power.
Nothing in her behavior says anything about her strength in the OP.
Again, this is just dead wrong. Mesaana is immediately described as pale and subdued when she is next seen after her punishment. She also all but begged Moridin to help free Semirhage, the only instance we see of a non-mind-trapped Forsaken show such obvious deference to the Nae'bliss. Demandred blows it off after a perfunctory moment, and immediately talks about how Semirhage would be afraid to kill Rand because of Demandred. Mesaana basically whines that Semirhage is a valuable Forsaken. Graendal, Sammael and Demandred all plot to take over as Nae'blss too ... we never hear such thoughts from Mesaana, only things about how Semirhage made her uneasy, followed by some bluster about matching up well against her.
Alviarin also immediately notes that the other Forsaken "flaunted" their strength but that Mesaana hid her ability, she had no need to do that when she was also masked and not acting as Danelle. Hiding her real strength was pointless to her disguise.
Shemerin came later, and reinforced the point. But the point was there from the beginning.
Just because Aes Sedai believe this doesn't make it untrue to how RJ told the story. Yes he made the point of showing it as wrong headed at times (i.e. Shemerin), but that doesn't change the fact that he wrote nearly every single powerful Channeler as strong willed. Go down the list of top 50 or so Channelers and you'll find that only a handful aren't completely forceful all of the time:
Mesaana
Moghedien
Asmodean
Shemerin
Sheriam (off and on)
Leane (off and on)
Theodrin
Yes RJ made a point of telling us that ranking themselves by Strength was stupid, but that doesn't change that he also wrote the powerful channelers as almost always strong willed people. Anaiya wasn't wrong based on the people we see in the books or from the Aes Sedai POV. And the Forsaken certainly consider strength as well as skill when dealing with one another so the fact that they are all pretty dismissive of Mesaana is rather telling. Especially since we know she's somewhat skilled since she was a teacher.
No one is saying that the Aes Sedai are actually right, only that it's not a faulty assumption based on how the characters in the books are actually portrayed.
Again, you are pointing out the exceptions that prove the rule. RJ had to go out of his way to illustrate that a woman like Sorilea was strong willed and could face anyone down and how the Wise Ones didn't consider strength in their hierarchy. And IIRC he originally thought about making Sorilea as strong as Cadsuane, but later changed his mind on that to make just this point stand out.
Bair, as a non-channeler, is rather irrelevant to the conversation. No one is questioning a powerful dreamwalker's strength of will.
But again... why does any of this have anything to do with OP strength?
She was an administrator of territories conquered by other Forsaken. She didn't conquer others or inspire personal fear the way the others did. Comparing her to Asmodean is pretty spot on actually, along with Moghedien these 3 came across as the weakest of the Forsaken IMO. She had not earned a 3rd name, she lied/deluded herself and hid behind shadows and more powerful allies ... it all goes toward an overall characterization. Reading her character she seemed to be weaker than the others.
It matters in the same way that a gifted athlete has more self confidence, she comes across as someone playing above her weight class, almost as if she didn't belong. Much like Moghedien and Asmodean did. Given that the Forsaken are all powerful channelers their personalities are part of how we understand their strength.