https://ncode.syosetu.com/n8406bm/ for webnovel raw
https://comic.pixiv.net/works/3714 for manga raw
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Novel is still ongoing but it appears that she will remain in Sengoku period. When she reunited with Azuma, he asked her if she wanted to go back or if she was willing to bury her bones in the Sengoku period. She hesitated but determined to stay since she already spread her roots in this timeline. Thus, he agreed to remain with her. Later, she is adopted by the Konoe clan as their heir (yes they gave her inheritance rights, but the current head is still active & doing politics for her). However, this brings up the question of Shizuko's spouse & after over 12 discussions between Oda, the Konoe head & Azuma, it is decided that Shizuko will adopt one of Oda's sons as her heir (named 46? because they're a twin & twins are considered bad luck - Oda wants Shizuko to overturn this notion. The kid is very shy due to abuse & mistreatment by his nannies - who Oda punished severely when he found out.)
The middle-aged man ended up accidently getting married to a young (teenage) noble lady (dude got drunk during an agricultural trip & made agreements he shouldn't have).
Shizuko & Azuma congratulated him on his second spring & he resigned himself to his new wife. However, because he is a very doting husband, he was considered excessively loving by Sengoku standards & all this affection turned his wife into a yandere type (but it's fine since he returned her love & had kids with her). The wife became one of the housewife workers that Shizuko was promoting (also one of the users of Shizuko's new healthcare system for pregnant women). She also is the only other person who knows that they are from the future (she was shown old photos of her husband & his first wife & kids).
Just to clarify
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Yes, it's because she's become too valuable to tie down to another clan & her logistics unit is mostly loyal to HER & not to Oda necessarily. Her marrying someone would result in a power conflict between her & her spouse since she wouldn't sit back & be a housewife nor would it be good for Oda & his vassals if she did that.
Her adopting an heir means that her prestige & all the feats she's accomplished will not end with her death & basically she's no longer a one-hit wonder & that makes her more important to the nobility. BTW she was adopted by the Konoe family because she was previously introduced as a bastard of the Ayanokouji clan & they've already admitted that they have no record of her. This adoption guarantees her her own power-base & noble rank that isn't dependent on Oda. Azuma was pretty mad when he found out about this & nearly cut down the previous Konoe head, who was also his old friend, until he explained to Azuma that he was doing this to keep Shizuko safe.)
The son she adopts (still named 46) is from Oda & one of his lower-ranked concubines (a maid I think? She died in childbirth as was common at the time for birth resulting in more than 1 children - which increased the stigma of twins being bad luck. I'm not sure what happened to the other twin or if MC adopted that twin too.)
46 is very reticent around her as he fears lowering her reputation & causing her problems & he only opens up after Shizuko's bodyguards tell him that it's fine since Shizuko is such a weirdo herself. There is a lot of cute parenting stuff involved. Later, when Shizuko's pet wolf (the first one) finally passes of old age & she goes into mourning (she asks Oda for a year off for the first time), 46 is worried about being able to comfort Shizuko as much as the wolf did. Her bodyguards tell him that nobody can replace that wolf for Shizuko, so they just need to help her out as much as they can.
As a fun fact, after Shizuko has the wolf buried on a mountain, Oda has a statue of her & the wolf built as a memorial & it becomes the center of a small but popular folk religion amongst the villagers living there - as they pray to the Wolf Lady for blessings in everything EXCEPT childbirth & marriage. :)
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Dude's not making any progress. He gets into a fight with Uncle A. when he pats Shizuko on the shoulder. Cue overprotective Uncle-ness.
During the marriage talks, Oda, Konoe & Uncle A all noted that there aren't any rumors of Shizuko being overly close with other males & the dudes around her just admire her.
Zero romance flags.
I have made a mistake with the names. Please swap in Katsuzou (Mori Yoshinari's son) instead of Ranmaru. They are different people & I mixed up their names (the whole "previous name" & "historical name" stuff confused me when I was translating). Nobunaga's son Kimyoumaru frequently ends up as Bizarre Maru thanks to google translate. Ranmaru doesn't show up until way later in the story.
Also it's Ashimitsu, not Azuma (again - blame google translate). Sorry about that.
I've read the entire raw webnovel up to 167 (& compared it to the currently released raw manga chapters on pixiv).
If you have any questions regarding future arcs, specific characters or situations in the manga, I can probably answer them (with like an 80-90% accuracy since I'm using google translate). :D