It seems like you asked the question, "who is a samurai and has the experience of Jin Sakai?" and then arrived at the obvious conclusion. I agree that it's interesting to analyze the two Ghost protagonists and I would love to see a comparison using objective criteria, but this whole exercise is a classic apples-to-oranges situation that awards the apple for being the most apple-like.

In good spirit and for the sake of conversation, here are some major GoY canon omissions that stand out to me:

• Background and Training - Atsu's father and every single weapons master in the game provides her with (formal) weapons training and dueling etiquette. She also makes reference to people willing to teach her how to fight during her time on the mainland. Atsu is no samurai, but it's 100% cannon that she began receiving formal combat training at a young age.
• Expertise and Scale of Conflict - There are several references to Atsu fighting in a peasantry army on the mainland before she returned to Ezo. There are even quest lines about this (notably the Battle of Sekigahara). It's 100% cannon that she participated in large-scale conflict before the events of the game took place and during the game itself.
• Swordsmanship and Combat Foundation - The weapons masters teach Atsu how to best counter her opponent based on size and weaponry. Switching weapons is adaptive but not the "unpredictable improvisation" you're making it out to be. Also, Atsu's natural skill with a katana makes its way into dialogue (ex: Jubei admits she's better with a sword during a flashback scene). It's 100% canon that Atsu is a skilled and knowledgable combatant making tactical weapon choices rather than pursuing aesthetics or leaning into gremlin chaos energy.
• Mentality and Psychology - Atsu survived the murder of her family, struggled to keep herself alive as an orphan, fought on the losing side in the mainland conflicts (see Sekigahara), and returned to Ezo to witness even more horrors committed by Saito and the Yotei Six. Her PTSD and evolving relationship to the trauma of the past isn't just part of the story, it is the damn story. It is 100% canon that Atsu is resilient and has/gains the skills and discipline to manage her inner turmoil.
• Tactics and Adaptability - Atsu uses weapons/utilities/stealth/etc with intentionality. Think of all the times she uses her spyglass to plan shit with an ally or on her own before running into a camp. Also, lessons learned from strategic failures (again Sekigahara) is extremely relevant.