When I look at the two images, I see with my eyes the white on the subject's head is blown-out (over-exposed) in both images. Downloading the image and asking LR to show those highlight clippings confirms what I saw with my naked eyes. In digital photography, you want to base your exposure on the highlights, especially in the critical image elements in the foreground / subject. I mention this in contrast to your stated approach of using the background (??) as the basis of the exposure.

Otherwise, double-thumbs up on the approach of simply counting the 'clicks' of the camera dials to maintain the same exposure after adding the ND filter.

I am a Nikon shooter and was excited to put the Tamron z 150-500mm lens on my z50. I was ready to do more wildlife and birds in flight photography until I spent some time with this beautiful beast….it is too darn heavy for me to hold still and I am not inclined to lug a tripod around when I get the urge to shoot some wildlife when I am close to nature. At 75 I admit I am not as strong as I’d like and holding that lens isn’t getting easier.

So I am returning it to Adorama today and exchanging it for the Sony cyber shot RX10 IV. I guess a bridge camera isn’t so bad….(right?)…..and it sure will make my sometimes forays into nature a little easier. I just hope I don’t have pangs of regret and envy when I encounter folks with those big, beautiful telephoto lens in the field.🥹