You can also use Python scripting in gdb:

(gdb) python import psutil
(gdb) python print(psutil.Process(gdb.selected_inferior().pid).environ())

This will print out a Python dictionary that contains the environment variables of the selected inferior.

Reference:

• https://sourceware.org/gdb/current/onlinedocs/gdb.html/Inferiors-In-Python.html#index-Inferior_002epid
• https://stackoverflow.com/a/52493842/5267751
• https://psutil.readthedocs.io/en/latest/#psutil.Process.environ

If you don't want external library (psutil), you can read from /proc/<pid>/environ as in the accepted answer.