Painless clicking is common and usually not a big deal, but I'm not going to tell you it's definitely nothing from a text description — if it changes, starts hurting, or you lose any strength or range, get it looked at by a physio rather than asking the internet.
That said, what helped me with an almost identical eccentric-only click:
- warm up the shoulder properly. Two sets of band pull-aparts and one light overhead set before the working weight. Mine clicked far less once I stopped starting with 40kg
- add direct external rotation work and face pulls, two or three times a week, light and high rep. Most of us press far more than we pull at that angle
- slow the eccentric deliberately for a few weeks. If the click happens at one specific point coming down, that usually means control drops off there
An asymmetry that appeared three weeks ago is worth watching, not panicking about.