I agree it really isn't all that much of a real world advantage. I honestly tried to replicate it myself to show here and the results were so close that I had trouble doing it.
There are a lot of reasons to like the D810, although the D800 is a sentimental favorite of mine(and one of the last I'd get rid of if push came to shove) as my first "good" DSLR and one that I'd not be ashamed to use in 2023 as my only camera.
To me the tangible advantages of the D810 are the much quieter/more refined shutter and the more comfortable hand grip. I didn't buy mine until used prices were around $1K, and bought it with the justification that I could use a very familiar camera along side my D800(not necessarily as a backup, but to for example avoid changing lenses in the field). The D810 became my main camera for the above mentioned reasons, but my D800 has never really gone out of use. I agree that it's worthwhile giving the D800 a serious look for cost savings, especially if you can find a lightly used one.
The D850 knocked both more or less out of rotation back in August when I got mine. IMO, it's possibly one of the best all around, well rounded DSLRs ever made. It is noticeably less noisy than D800/D810 and gets even better if I downsample it to 36mp. The AF is superb(nearly D5 levels of performance, although my D5 seems to lock easier and track a tiny bit better esp. in 3D tracking). It's a do it all camera with a more than acceptable frame rate for most uses with the grip+EN-EL18. I don't notice an image quality difference most of the time since I handhold a lot, although it did push me over the edge on buying the newer 24-70 f/2.8E. If I didn't have one and wanted to buy a DSLR in 2023, I'd pick a D850 again.
B&H had a similar deal during the holiday season about three months ago. Back then it was the 325G card plus a CFx B/SD dual card reader for $250. This time it is the card alone:
Delkin Devices 325GB BLACK CFexpress Type B Memory (bhphotovideo.com)
This older thread has the previous deal, long expired: https://www.photo.net/forums/topic/536791-nikon-usa-black-friday-deals-2022/#comment-5757141
Absolutely go with what you see as the image you want! Anything I say is just an idea.
An alternative that also de-emphasizes the house is to tone it down. I don't know what you use in post, but I do this very often in Lightroom, which makes it very easy to put a mask on an object such as this.
I have a Wacom Intuos black with bluetooth and pen. CTL4100WLK0.
I've tried it on my Windows (Dell) desktop and just didn\'lt get into it so its been sitting in its box for two years. I could let it go for $40 if you or anyone else is interested.
I once bought German made slippers through a London department store because that particular model was not available in the US. It only cost about $17 for shipping to NYC, maybe less, and arrived very quickly.
Of course, you have the VAT and import taxes. But it might be cheaper anyway. You never know.