Yes, there are some. You can check out fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'sakura wife kakashi' on those platforms and you'll likely find a variety of stories. Some might focus on their relationship development, while others could be more adventure - based with their relationship as a side - plot.
Archive of Our Own (AO3) is also a popular option. It has a tagging system which makes it easy to search for specific types of fanfictions like 'sakura wife kakashi'. There are often detailed descriptions and reviews to help you decide which ones to read.
Anko Mitarashi could be a good candidate. She's strong -willed and has her own set of skills. Her somewhat wild personality could contrast well with Kakashi's more reserved nature. They could have met during a mission and over time, developed feelings for each other.
One interesting plot idea could be that Kakashi's wife is a powerful ninja from a hidden village that was once an enemy of Konoha. She has to prove herself to the villagers, especially Naruto who is initially suspicious. Another idea is that she has a special ability related to sealing jutsu which helps in a major battle against a new threat. And perhaps she has a past connection to one of the Akatsuki members which adds a layer of mystery.
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
In such fanfiction, the Kakashi OC often has unique physical features. For example, they might have distinct hair color or eye shape that sets them apart.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
Often, Naruto is paired with Kakashi in such fanfictions. Their bond from the original series can be explored in new ways in the context of Kakashi's reincarnation. For example, Naruto might be the one to discover Kakashi's reincarnated form and help him adjust.
Kakashi could use his Sharingan to analyze Obito's moves and find a weakness in his defenses. Since he has the Sharingan, he might be able to predict Obito's attacks and counter them effectively, eventually finding an opportunity to break free.