I recorded a 20 minute time-lapse of my AOD, and to my surprise, Apple isn't shifting the widgets at all. I expected them to slowly move around by a few pixels to minimize burn in over time. The clock moves pretty much every minute to stay centered with different number widths, the date will obviously display different characters in different places every day, and the Astronomy lock screen I tested with seems to very slightly rotate the earth every 5 minutes, but a lot of widget elements remained completely static, which increases the likelihood of burn-in.
My Apple Watch shows me plenty of widget information anyways, so at this point, I've removed all widgets from my default lock screen. I do want to have a shortcut widget to open Halide from the lock screen, but I would usually only need that when out and about, so I set up an Away From Home Focus mode that adds that widget to my lock screen whenever I'm not home.
I also set my lock screen to solid black for now to save battery and reduce the potential for burn in over time. I work from home with my phone sitting on my desk all day, and I like that the AOD can show me notifications, but I would be a little worried about a photo being displayed there all day long, every day, for years. I very rarely change my lock screen and home screen wallpapers (like once per year sometimes), and plan on keeping this phone for at least 3 years, so that would worry me.
If you plan on keeping this phone for 2 years or less, and especially only 1 year, then you probably don't even need to worry about burn in.