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The Tsaritsa can smell Tartaglia's bullshit from a mile away. She knows Tartaglia wouldn't voluntarily marry anyone for anything other than love. And he wouldn't marry anyone involuntarily, unless she ordered him to, and since he was a loyal Harbinger, he would've followed her order, so it wouldn't have been involuntary after all.
She certainly didn't order him to marry Morax as part of his mission in Liyue. Which means Tartaglia decided to marry Morax on his own free will. He didn't ask for permission, no, he merely informed her as protocol demanded. And Celestia knows that everyone would've known if Morax, presumed dead or not, had been displeased or horribly offended with Tartaglia's marriage proposal.
No. Instead, by all accounts, all the reports she received about her Eleventh indicated that the marriage proposal had gone without a hitch. So well, in fact, that they'd immediately eloped, without anyone knowing, until the couple had gone on a month-long retreat away from public eyes and everybody noticed their absences.
Those are not the actions of a couple who married for political reasons. Why would the infuriatingly politically-savvy Morax knowingly marry a mortal human, who ranks below him, who belongs to a different country, who serves a different archon?
The only logical conclusion is that they married for love.
Sure enough, she'd received reports of Zhongli moving into Childe's home after they returned from their retreat. To this day, Liyue continues its prosperous, peaceful existence, which she takes as a sign of Zhongli and Childe's happy marriage. Otherwise, if they truly quarrelled, if they found themselves truly incompatible, Morax's stone spears would've pierced the land once again, and Tartaglia would have raised unstoppable floods, at the very least, until his inevitable demise.
And yet here Tartaglia is, not even a century into his marriage, volunteering to go on a hunt for her Eight that might take an inconsiderable amount of time, knowing that it would keep him away from Liyue. Away from Morax. In addition to the fact that he'd been forced to go to Inazuma on so little notice that she doubts he'd been able to tell Morax goodbye.
Ah, so that was it. Perhaps Tartaglia was merely dreading the fallout of his unplanned departure. He had nothing to worry about, of course. Morax was not unreasonable or childish. He knew what it meant when duty called, and would forgive Tartaglia if her Eleventh apologizes sincerely.
She's glad she had cut off Tartaglia's enthusiastic bid to look for Scaramouche. It would not do to test Morax's patience, nor his possessiveness over his husband. Sudden emergencies, Morax would forgive, for he was reasonable to an extent, but extended, unplanned absence... No, she wouldn't risk it. Ordering Tartaglia back to Liyue is the right thing to do.