Clarity required on blank warranty cards

Hi Everyone,

Long time lurker, first time poster - and yes, I've used the search function for my question and that's exactly why I am making this post.

I am looking to buy a second hand Omega 3861. The seller has the receipt of the watch purchased from Omega but the warranty cards are 'completely' blank.
One post I found here suggested that OBs have now accepted receipts of purchase in lieu of warranty cards for servicing. However, they recommend that ADs/OB fill out warranty cards regardless.
Other posts have commented on some warranty cards having only serial numbers vs date of purchase vs only AD stamp, and/or some variation.

My take from reviewing old threads is that AD/OB practices are heterogeneous in what is filled out, especially after 2021. My questions are:
1. Is a *completely* blank card suspicious?
2. Would a receipt of purchase be truly enough here for servicing? My concern is that it will clearly not have my credit card or personal info on it, but that of the previous owner.
3. Is it outrageous of me to ask the seller to go back to where watch was purchased to have the AD fill out missing info on the card?

Some advice on how to proceed with this is appreciated. It's important for me to buy the watch with the warranty. For what its worth, the seller himself seems to have positive reviews on this particular forum but even he is not sure about why the card was left blank.

Thanks everyone,
How would I know that the receipt I have is the same one that belongs to the watch? Is there a serial number on the receipt?

It is better to check with your local Omega Service Centre, my recent check with them about warranty issue when make online purchase was "As long as the warranty card is duly filled up with the details of the boutique as well as the date of purchase, the warranty card will be valid for a 5 years period."