@PascalVezina
The units in Pro are set at the project level. If you would like to have the units set in the Map level, you can submit an idea in the ArcGIS Pro Ideas location: https://community.esri.com/t5/arcgis-pro-ideas/idb-p/arcgis-pro-ideas
Why do we store the measurements in the units of the spatial reference?
1. It allows you to exchange data with others knowing that the units are correct
2. It allows us to do the correct unit conversion when you project the data between coordinate systems that use different linear units.
Why storing units on the record is problematic?
1. If you provide a subset of lines to someone - they will not know which units the data is in.
2. Too many places to store units (project, record) will make it confusing. Which one trumps the other? why do I don't see my updates reflected?...
If you want to see different units labeled in the same map, you can add a 'LabelUnit' field and use Arcade to convert it to the target unit of interest + add a postfix to note which units those are in.
If you want to set the unit on the record and have it trickle to the associated lines, you can use an Attribute Rule for that. Every time you create or modify a line it can use the CreatedByRecord GUID to find the record and copy the unit. You can also apply the same logic to scale and rotation.
We also had a few meetups on Arcade and Attribute Rules that might have shown similar examples and have been uploaded to the parcel fabric community.