your response to @MakeShiftWings: thanks for clarifying about the game/scene view thing! I had my gave and scene view on top of each other, didn't realize having them both open keeps scene view from jerking about.
I'm running 3.4.9, though I don't see anything in 3.5.0 that would change this.
So I made a sprite and label, and as soon as I anchor it the first "Dimensions" input grays out (pic1), so I need to disable anchoring, resize the sprite, and re-enable it to get the position, or as OP states, set the right anchor to the same target and add the offsets together for the offset amount. It's not too terrible an inconvenience, really, but just seems like an oversight.
Also a small strange thing, are anchors supposed to take multiple "refreshes" to resize correctly? I put a sprite behind the label anchored to it, and changed the contents of the label. I have to grab the side of the scene view and "shake" it (resizing the scene view), and the elements (sprite anchored to label, label's anchor to the left sprite) will sort of shimmy back into place. It ends up correctly so this isn't really a problem, but might explain why getting the dimensions of anchored sprites sometimes returns unexpected values (that is, grabbing the value before the anchors have finished moving back into place).
For clarity: those label# pictures were taken with the Snipping Tool, and by taking a picture, clicking on unity to cause another "refresh" that moves the anchors a bit, then taking another picture, etc.
I also tried this with just the left sprite and label and it's the same thing, it takes a few refreshes for the label to slide back in place.