>Status: Asset (uncooperative), Dormant, Emissary Level Approval
From this we see that he is an asset (ie a valuable possession) but is uncooperative, likely devaluing him somewhat, and is considered dormant with "emissary level approval." It is not made clear what exactly the latter terms imply, but from later text we can extrapolate that it means he is not being given orders actively anymore EXCEPT with the direct approval of his handler, First Emissary Elenwen (the Thalmor ambassador to Skyrim).

>Description: Jarl of Windhelm, leader of the Stormcloak rebellion, Imperial Legion veteran
I think we're all clear on this and don't need to go into further detail.

>Ulfric first came to our attention during the First War against the Empire, when he was taken as a prisoner of war during the campaign for the White-Gold Tower.
This too, but I highlight this for the sake of noting that he was taken prisoner by an organisation that had already brutally murdered POWs and was at their mercy, for later reference. Outside of this specific text it must be noted that at this time the Stormcloak rebellion did not exist, he was just a potentially influential legionaire who knew a bit about the thu'um.

>Under interrogation, we learned of his potential value (son of the Jarl of Windhelm)
Now we learn that he was not even the Jarl at this point, but merely held the promise of one day holding a high public office in Skyrim if he was not killed.

>and he was assigned as an asset to the interrogator, who is now First Emissary Elenwen.
Whoa! Alarms going off! He was, at this point, as a prisoner who was the son of a Jarl, considered an asset (a valuable possession). Did they intend to hold him ransom? Of course not, they assigned him as an asset to a Thalmor officer (his interrogator). This should erase any doubt that he was considered a valuable possession of the Thalmor, not merely someone who happened to be acting in a way that was advantageous to them.

>He was made to believe information obtained during his interrogation was crucial in the capture of the Imperial City (the city had in fact fallen before he had broken)
We can glean three important facts from this. First, through interrogation (and presumably torture) Ulfric was broken and gave away state secrets, proving that the Thalmor had control over him. Second, for some reason Elenwen felt it beneficial to his cultivation as an asset that he be made to believe he was responsible for the fall of the Imperial City- Meaning this was part of some ploy to manipulate him into acting as the Thalmor desired. Third, Ulfric believes he is responsible for the fall of the Imperial City (and by extension the White-Gold Concordat that basically shits on his people's culture).

>and then allowed to escape.
This is a callback to that part where I pointed out that the Thalmor had killed POWs in the past. BEFORE he led the rebellion or was even Jarl, they spared his life because of his value as an asset, further cementing that his value to the Thalmor is not incidental or merely because he fuels the civil war. At this point they were playing cat and mouse with him as well- They did not "let him go," they "let him escape," as in, let him believe he had escaped imprisonment of his own volition, playing into their hand all the while.

>After the war, contact was established and he has proven his worth as an asset.
Simple and clean here, we've been over this like four times already. Elenwen contacted him, he realised the Thalmor still knew where he was and that he was still her bitch, he did as the Thalmor said (possibly because what they wanted seemed to benefit him as well, or because he still thought he could outsmart them- when the only way he can ever eventually do so is with the help of a literal deus ex machina in the form of the last dragonborn applying the fury of Akatosh to the Legion; both of those are only conjecture though, much like your entire argument has been, so this is tangential).

>The so-called Markarth Incident was particularly valuable from the point of view of our strategic goals in Skyrim
This was an attack on a renegade populace of forsworn, not on the Empire. Ulfric was recapturing the city for Skyrim (and by extension the Empire, which also means he brought it under Thalmor control as we see it during the events of Skyrim), superficially on the condition that Talos worship would be allowed there despite breaking the terms of the Concordat. In fact, the reason this was valuable to the Thalmor is that it enabled them to occupy the city without breaking the terms of the Concordat themselves, to oust the Talos worship that would ensue. Again, this demonstrates that Ulfric's only worth to the Thalmor is not in weakening both the Empire and his own loyalists but in using military might and the cunning of Elenwen to gain influence for the Thalmor.

>although it resulted in Ulfric becoming generally uncooperative to direct contact.
This has two implications. First, as if it still needed to be said, it confirms that his actions in the Markarth incident were him carrying out Elenwen's orders, not him acting independently (which is end of discussion as far as I'm concerned, that is literally what this argument is about)- he here BECOMES generally uncooperative, meaning he was hitherto cooperative. The word "generally" is also important, because it means he is not entirely uncooperative. The phrase "direct contact" is likewise important, as he might still be cooperative in other ways. Second, it of course reveals that he DID become generally uncooperative to direct contact, just as it says. But wait, there's more

>Operational Notes: Direct contact remains a possibility (under extreme circumstances), but in general the asset should be considered dormant.
Simple enough. He may be showing signs of rebelliousness, but he and the Thalmor both still know they're technically allies- or more accurately, that he belongs to them. As later text will reveal, "dormant" does not mean he is not actively benefiting the Thalmor. As I think we're all agreed on, he benefits them by prolonging the civil war if nothing else.

>As long as the civil war proceeds in its current indecisive fashion, we should remain hands-off.
Here it is revealed that "dormant" simply means they are taking a hands-off approach because he is carrying out actions that benefit the Thalmor even without direction. However, this comes with a very important condition- If he stops doing so, they will stop being hands-off and resume control. He is absolutely still theirs (at least as far as they're concerned, and they seem to know what they're talking about), it just isn't worth the effort to try to micromanage him when he's doing what they want regardless.

>The incident at Helgen is an example where an exception had to be made - obviously Ulfric's death would have dramatically increased the chance of an Imperial victory and thus harmed our overall position in Skyrim.
This confirms that the reason the Thalmor were at Helgen was to prevent Ulfric's execution. What exactly they planned is not known, of course, because Alduin showed up and created a distraction before they could. It does confirm that they did still intervene, which explains why, if you go the Stormcloak route at the beginning, none of the soldiers have seen Ulfric- The Thalmor somehow smuggled him out another way.

>(NOTE: The coincidental intervention of the dragon at Helgen is still under scrutiny. The obvious conclusion is that whoever is behind the dragons also has an interest in the continuation of the war, but we should not assume therefore that their goals align with our own.)
irrelevant to this discussion, only confirms that the Thalmor are as confused by Alduin's return as almost everyone else

>A Stormcloak victory is also to be avoided, however, so even indirect aid to the Stormcloaks must be carefully managed.
This merely cements why they are taking a hands-off approach (that the civil war benefits them by weakening both parties through attrition, not merely weakening the Empire), while also confirming that they have been sending aid to the Stormcloaks without meeting Ulfric in person, again playing on the distinction between "direct contact" and just "contact."