There is no time period from 5-15th century that this would make since
If we assume the only armor is what we see, then that armor is mostly ornamental. But's let's be kind and assume that all that flowing clothing we are seeing is actually Surcoats, and that under that cloth is actually some manner of mail or plate armor.
Even taking this liberty, you can see from the parts of the armor that is has lots of gaps in it making it comparable to 12th century transitional plate armor at best. By the 13th century, European armorers got pretty good at closing up all the gaps in armor making it really hard for an accidental strike to get between the plates.
This armor also has the flaw of being held together by external lacing which is vulnerable to being cut. By the 13th century, European plate armor was fully articulated plates that were riveted directly to one another, or brigandine which riveted plates to a solid sheet of fabric or leather. Both designs were much better than laced plates.
So, if 13th century or later Europeans and Japanese met, it is much more likely that the Japanese would be copying European armor, not the other way around. This means that your POD would likely have to be before the 13th century for that armor to compete anywhere outside of a fashion show. While I could see the kimonos and conical hats taking off as every day attire, the armor aspects, not so much.
The styles of Japanese swords shown are useless against most styles of European armor between the 10-15th century. While there have been many tests showing a katana penetratingly the butted mail often used in Asia, the Europeans almost exclusively used riveted mail. Every penetration test I've seen of a katana vs riveted mail shows that it can not get deep enough to cut through the arming coat. Before the 10th century, partial mail was common enough in Europe that more cutting focused swords like the katana still made since. But, from the 10th century onward, most professional soldiers fought in full-body mail or plate armor that the Katana would be unable to cut through. This change in armor is why knights transitioned from cutting swords like the 8th century Charlemagne sword to the pointer styles of arming swords and long swords you see in the middle-late medieval period.
Keep in mind that the Europeans encountered a comparable styles of swords like the Muslim scimitars in the 11th century, but despite being impressed by the quality of steel, they did not widely adopt the shape because crusader swords were much better at dealing with an armored opponent. This further pushes back your POD to likely have to be before the 10th century for those swords to be practical.
The Textiles & Ornamentation:
Before the 13th century, pretty much all Medieval European cloth was course, thick, and had relatively low thread counts. Even if Europeans were exposed to this style of Japanese attire, it is unlikely that most people (even many lords) would have access to it since their own textile industry would be unable to reproduce it.
Dates of Origen:
So, for a variety of practical reasons we can already see that adoption is unlikely (but not impossible) at any point in medieval history, but the real reason you would never see this happen is because a lot of what you are seeing simply did not exist for most (if any) of the medieval period.
The elements of Japanese Ō-yoroi style armor did not exist until the 10th century and were not actually common until the 13th century. Furthermore there is a lot of elements of Haraate armor that shown did not exist until the 15th century which rules out Europe getting these styles from Japan before they would have been obsolete in Europe. The older Japanese Tanko style of plate armor was around as early as the 5th century, and I could easily see it influencing the Early Medieval period, but Tanko armor is distinctly not represented in these pictures.
Also, these images show warriors armed with Odachi, a 14th century sword, and Katana, a 15th century sword. Before the 14th century, the Japanese generally used Chinese styles of swords similar to the Dao or Jian. Also, the styles of European swords that had those extra long cruciform cross guards did not emerge until the late 15th century. At most you could interpret these pictures as depicting the type XIIa Longsword (allowing for some artistic license) which emerged in the 13th century.
Also, many of the European styles like the lapels on some of the shirts, and the styles of some of the boots did not exist until the 18th century putting some of these pictures 100% outside of your desired time period.