Elite Controller Left Trigger Jumps From 0 Straight To 1, Is It Broken?

Before anything else, turn the controller over. The Elite Series 2 has trigger locks, small sliders on the back beside each trigger, with three positions. In the full position you get the normal analog pull. In the shorter positions the trigger's travel is physically limited, and in the shortest one a very short pull with a click registers as a full press. In the test that looks exactly like what you describe: 0, then straight to 1.00.

The locks are easy to knock during play or in a bag, and the click makes it feel as if something broke. Your right trigger being smooth fits too, since only one lock moved.

If the lock is already in the full travel position and the trigger still jumps, look at the profile next. The Xbox Accessories app lets you adjust trigger settings per profile, so a profile with extreme trigger dead zones can produce the same 0 to 1 behaviour. Switching profiles with the profile button, or checking the trigger settings for the active profile, rules that out.

Only if both of those are normal would I suspect hardware, and with an Elite a warranty claim is the right route if you are still covered.