After comments - & some cajoling from "management" to put my money where my mouth is (just kidding;) I had a deeper look at this.
Bear in mind, I'm fumbling through this as I really don't ever play with LUTs, nor 'portable styles'.

Yes, you can save a LUT in various forms from any set of adjustment layers, however, the result may not be quite what you thought. Playing with an image from another question, I generated a red-green shift, then vignetted the mask, so the centre stayed untouched.
This was based on work done for Creating a LUT in Photoshop with a Vignette & using an image from Why does flash make a brass subject look grey? that I just happened to have open.
These are all just screenshots, quality unimportant. Click for slightly larger

I saved the result as a LUT, in all 4 available file-types (not having any clue what they all do)
I then re-imported each to see what happens. I got variations on a theme of 'wtf'.
Not what we're looking for. Re-adding a vignette to this isn't going to help.

So, after poking around a bit, I decided to save my one adjustment layer, in PSD format.

Much better, though still a bit awkward. I can now re-import my hue-shift/vignette layer & then drag it to a new image.

So, I managed it, but not particularly elegantly. I'm open to better ideas ;)

Having fought with this for an hour or two, in retrospect it's really the kind of task I wouldn't do in Photoshop. I'd give it to one of the 'modern' editors like Luminar or Affinity Photo, with their 'instant look' presets - in comparison, it seems what they're designed for. Photoshop isn't.