System Information
Operating system: Linux-5.4.0-65-generic-x86_64-with-debian-bullseye-sid 64 Bits
Graphics card: GeForce GT 520MX/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 390.141

Blender Version
Broken: version: 2.91.2, branch: master, commit date: 2021-01-19 16:15, hash: rB5be9ef417703
Worked: (newest version of Blender that worked as expected)
hey i try to update, but linux did it well alone... not seen broken, but usable ;)

Short description of error
[WRONG edge lenght after SCALE ]

Exact steps for others to reproduce the error
[use anything in edit mode.
NOTE that the lenght is ok if you stay in edit mode and rescale !
make edge lenght visible.
back to object mode
then rescale the object even a line. then relook the edge lenght in edit mode:
OOhhh the same lenght even rescaled it is !]
[think it's not a .blend file .. this problem is a long story pb not solved. But now it's enough, i must say it. ;)
so i join 2 files (.jpg) of demonstration] - if you can't reproduce the problem.. i'll try with other file and join it .. oh .. i can now .. ;)
no need to join, i test with an other file: it's reproduced !
0 - create a base plane (2x2m)
1 - edit

2 - note the measures - lenght and also surface too !
3 - back object mode
4 - now rescale the plane
5 - back edit mode
6- constate the SAME lenght value - no rescaling