Verifying authenticity of a secondhand Rolex

[Speeding944T]

I recently purchased a 2023 Rolex Datejust 41 from a vendor in Nakano city (west side of Tokyo, Japan). The vendor name is Brand Bank (ブランドバンク中野店 in Japanese). They seem to be a legit store with another branch in Ginza, and they also have an 80k subscriber, active Youtube channel in Japanese advertising their latest inventory. However, they only have limited Google reviews from Japanese sellers, not from buyers.

Brand Bank in Nakano is a small shop and is oddly located in a corner of the basement floor when most of the larger and well-known shops like Jackroad and Betty are on the 3rd floor of Nakano Broadway. The watch came with what seems to be an original box, and the international guarantee card has a serial number matching the watch’s rehaut. The white tag that confirms the original dial was missing, but the shop staff says that none of the Rolex watches in Japan come with the white tag. Not sure how true that is, but I’ve heard that some AD’s as of recently are keeping the white tag in other countries as well.

From what I can tell, the watch is 100% authentic. I can’t find anything that seems off, but considering how much money I spent, I would really like to have verification from an expert. This is my first Rolex purchase and seeing some of the ridiculously similar fakes keeps me up at night wondering what if. The shop staff that sold me the watch recommended taking it to a Rolex AD and having them do the verification if I’m genuinely concerned.
All of this is a first for me. Is it normal for people to bring grey market watches to a Rolex AD for authenticity verification? Is the AD going to blacklist me from future watch purchases if I come in with a grey market watch? I guess it depends on the location, but do AD’s charge for doing an authenticity verification and are they going to want to hold the watch for several days/weeks? I’m interested to hear everyone’s recommendations.

Picture of the watch added as an attachment. Hopefully that shows up on my post.