The requirement
A receptacle GFCI manufactured after 29 June 2015 must run an automatic test of its ground-fault sensing at power-up and at least every three hours. When the test fails, the device must either open its contacts and refuse to reset (lock-out), or give a clear visual or audible indication, or both. Most makers chose lock-out plus a light.
The lights
Conventions vary by brand, but the common pattern: a steady green light means power on and the last self-test passed; red or amber means the device has tripped, failed a self-test, or is miswired; no light with power present usually means end of life. Read the label on the face — it is printed there.
Do you still press TEST?
Yes. Self-test exercises the electronics; the button also exercises the mechanical latch and confirms the RESET returns power. The manufacturers' instructions say monthly, and how often to test explains the job-site schedule.
Breakers and portables
The 2015 self-test rule is written for receptacles. GFCI breakers and portable devices are covered by their own clauses; many recent portable in-line units include an indicator and some include automatic monitoring, but the button test remains the required check on a job site.
Replacing old units
A receptacle installed before 2015 with no indicator light is not defective for lacking one, but it cannot tell you it has died. When it fails the button test, or when a bathroom is being redone anyway, a self-test replacement is the small cost that ends the guesswork. Wiring is the same (line vs load).