Way I can find out when a shapefile was created or last updated

A bash solution for this purpose. As stated by other in comments, this recipe considers that dates on your file system/OS can be trusted

# Clean to be able to repeat the script multiple times
rm *_meta.txt
rm summary.txt

# Double loop to get basename for shp then from this basename
# get all files as your shp various files dates may differ
# Sort by date each file with same basename with `stat` command considering
# %y   time of last modification, human-readable
for shp in *.shp;
  do tmp=$shp;
     tmp=${tmp##*/};
     tmp=${tmp%.shp};
     for entry in $tmp.*;
       do echo $(stat -c%y "$entry")" $entry" >> $tmp"_meta.txt";
     done;
done;

# Loop each file with creation date for each
# For instance, myfile_meta.txt would contains
# 2018-05-21 09:24:36.000000000 +0200 myfile_meta.cpg
# 2018-05-21 09:24:36.000000000 +0200 myfile_meta.dbf
# 2018-05-21 09:24:36.000000000 +0200 myfile_meta.prj
# 2018-05-21 09:24:36.000000000 +0200 myfile_meta.shp
# 2018-05-21 09:24:36.000000000 +0200 myfile_meta.shx
# From this file, take the last one, the more recent
# and append it to summary
for meta in *_meta.txt;
  do sort $meta | tail -n 1 >> summary.txt;
done;

Use ogrinfo. However, it does not know if the editing software has been updating the last update metadata in the .dbf file. GDAL and QGIS do update it.

ogrinfo test.shp -al -so
INFO: Open of `test.shp'
      using driver `ESRI Shapefile' successful.

Layer name: test
Metadata:
  DBF_DATE_LAST_UPDATE=2020-11-24

See also https://gdal.org/drivers/vector/shapefile.html

Open options:

DBF_DATE_LAST_UPDATE=YYYY-MM-DD: Modification date to write in DBF header with year-month-day format. If not specified, current date is used.

and

Layer creation options:

DBF_DATE_LAST_UPDATE=YYYY-MM-DD: Modification date to write in DBF header with year-month-day format. If not specified, current date is used. Note: behavior of past GDAL releases was to write 1995-07-26

Past releases mean several years old GDAL versions.