I'm using QGIS 3.2 and want to manually move a few labels on a layer but when I try to use the move labels tool I can't move them. I can however rotate and change them using those tools. I looked in the Auxilliary Storage and it seems like the move tool is not creating new fields for the movement whereas the rotation and change tools can. Is there any reason the move isn't working while the others area?
This is a known bug. It was reported for QGIS 3.0.3 and was fixed, but it re-appeared in 3.2.1.
Your options are:
Wait for a bug fix.
Revert to QGIS 3.2.0 - download old version of QGIS here.
Use a static field for data-defined label positions.
Create fields called "LabelX" and "LabelY", with Field Calculator expressions
y($geometry), respectively. Set these fields to control the label position.
With the layer in editing mode, try using the Move Label tool - hopefully it will re-position the labels and change the "LabelX" and "LabelY" values. If not, you'll have to position your labels by manually editing the values in these fields.
I find that this problem occurs in cases where you have selected "Store Data in Project", and you have modified the label using the "Change label" button on the tool bar. So one can either go back to the old way where you do not "store data in project"; or if you are storing your data in the project, and you need to modify a label, make the change by opening the attribute table and changing it there. Then everything seems to work out ok!
I don't have enough reputation to comment on @MaT's answer, but this is what worked for me with QGIS 3.18.3. I am posting just to add that I noticed the issue only appeared on layers where I pasted label styling from another layer, so I supposed this might be a feature to make sure the pasted styling stays untouched, but it's not exactly trivial.