I don't know how QGIS writes and reads CRS information, but currently there is a significant issue with non-EPSG codes.
A short answer to how to know if your file has a valid CRS defined, until this problem is resolved, is to verify if the code is registered in https://epsg.org/search/by-name.
If the code is registered, the file will have a valid CRS. If not, no.
Some time ago I had been observing that I had many custom CRSs automatically generated, but I did not know what was due and I thought it was normal. Until I saw this question. Since then I began to investigate a little about the subject, with my limited academic resources in computer subjects.
Note the following behaviors from the console:
C:\>cs2cs -v +init=epsg:102711
Using from definition: init=epsg:102711
Rel. 5.2.0, September 15th, 2018
projection initialization failure
cause: invalid projection system error (-9999)
program abnormally terminated
C:\>cs2cs -v +init=esri:102711
# ---- From Coordinate System ----
# Cyl, Sph&Ell
# +init=esri:102711 +proj=tmerc +lat_0=38.83333333333334 +lon_0=-74.5
# +k=0.999900 +x_0=150000 +y_0=0 +ellps=GRS80 +datum=NAD83
# +to_meter=0.3048006096012192 +no_defs +towgs84=0,0,0
#--- following specified but NOT used
# ---- To Coordinate System ----
#Lat/long (Geodetic alias)
# +proj=latlong +datum=NAD83 +ellps=GRS80 +towgs84=0,0,0
proj database this is an Esri code, and it is defined in the
The WKTs written by QGIS for these CRSs are not recognized as valid at the time of reading.
In a shapefile, the WKT is written in the .qpj file, and the last line says:
AUTHORITY["Esri","102711"]. If that line were changed by
AUTHORITY["EPSG","102711"], the file would have a valid CRS for QGIS. In Linux are written a little different, I imagine that another version of a library will be installed. But is invalid too.
In a geopackage, the WKT is written in the definition field of the gpkg_spatial_ref_sys table. Yo can see it from Database > DB Manager > SpatiaLite > New Connection connecting to the geopackage. The attribute can be updated by SQL queries. But I do not intend to manually edit each written attribute in a way that can not be read as valid, that is, the CRS of each file that does not correspond to an EPSG code.
I would rather have it resolved by the developers. This bug ticket was opened at the time. Contributions and details that I do not know and can be corrected, are welcome.