Would it be possible to implement a "Dark Mode" on the Physics Stack Exchange as is being trialed on the Stack Overflow? I personally would prefer that viewing mode. Use the upvote on this comment to express your support if you'd like this feature because it appears they chose to introduce this feature on the Overflow SE due to popular demand.
Is it possible? Sure.
Is Stack Overflow (the company) going to invest enough developer time to produce this (and commit to continue to invest enough developer time to maintain it, which is an even taller barrier)? Who knows.
People have asked for this, repeatedly, both on Meta Stack Overflow and on Meta Stack Exchange, over the better part of the last decade. Whether SO will go forward and use the opportunity to invest on the broader network (particularly now that they've invested enough to make dark mode in SO a reality, and given the investment early last year in unifying the theming for the network sites) is currently an open question.
In addition to that, as you noted in the comments, the blog announcement itself states that
For now, we have no plans to bring dark mode to the many sites across the Stack Exchange network. Many of the designs on our sites have been around long enough that converting them to dark mode would require redoing the artwork completely. We would prefer to avoid giving anyone across our network a substandard experience and we don’t want to change those elements without the input of these communities.
which leaves the door at least a little bit open for this to be extended to network sites, but sets a clear bar in terms of the amount of work that would be required for this.
(To be honest, I'm rather surprised that they're saying this, since the uniform rollout of this kind of feature was sold as the advantage for the loss of theming during the Great Theming Debacle of 2018 (see here and subsequent posts for details). But then again, they know better, I guess?)
To be honest, I don't thing our site has the clout to request this. We're the 20th site by traffic, down from SO by a full two orders of magnitude. It took the most-requested feature on SO the better part of a decade to get addressed. It would take a close-to-unanimous, vociferous request for the SE devs to put any kind of priority into this.
Instead, the best bet if you really want this is to look for voices calling for dark-mode availability on places with more traffic and more clout on the SE network (my first guesses would be Software Engineering, Serverfault and Super User, but none of them seem to have such requests) and lend your support there.
... or, if not, to try to do it locally using Stylish or the other tools mentioned here.