(Specifically replying for hep-th mentioned by the author.)
I would say that the daily arxiv read habit becomes more useful after a few years in the field by which time you understand what papers are roughly about and whether they are interesting for you just from the title, abstract and author names. Once you know what the current state of the art is, it can be a good way to keep up to date on the most recent developments.
The problem with looking at these at the start of your PhD is that these papers containing the newest developments will build on other papers and will assume you are already familiar with a lot of the "most important" papers.
Therefore I would myself instead recommend reading a review on a subject you want to study in depth (probably the subject of your first research project) and read that along with the important papers cited in it.
I would also expect that your supervisor would give you a list of important papers to read and you should read those along with the papers cited in them which you will likely also will have to read in order to understand them.
After this you will likely be able to recognize, understand, and appreciate the newest papers appearing on arXiv in this specific sub field.
As your domain knowledge grows this way you can try picking up reviews on slightly different subjects and this way slowly expand the areas of high-energy physics that you understand enough so that it actually becomes useful to read new papers on the arXiv on these subjects.
(Of course a great alternative for reviews as a starting point are lectures at your university or at summer school's and such.)
"I would be surprised if there aren't any "latest cool things in this
particular area of physics" with easy-to-read formatting: an Instagram
post, a podcast, or even just a rich text email."
I have never really heard about such a thing. There might be popular science things that are absolutely terrible which I would advise you to avoid. For real research I don't think this exists. I think you are overestimating how big any specific sub-field in hep-th is. There will be maybe a 100 people in the world working on the things you will work on. Not exactly enough to build critical mass for a social media audience. There are some blogs that are somewhat popular but they obviously don't discuss all important papers (probably even none within your subfield). I usually hear about http://resonaances.blogspot.com/ although I think it is closer to hep-ph. There used to be a somewhat popular blog by a very controversial ex string theorist but I think it was taken down.)