My commuter bike has a 7-speed Tourney groupset with thumb shifters. When commuting today, I arrived at the office and shifted down a few gears before parking the bike as usual. I noticed that the rear derailleur was on the largest sprocket and didn't move on shifter input, anymore. I still had the clicks and the gear indicator moving but there was no action, the levers felt a bit light.
It is an older bike (bought in 2016), but since Tourney hasn't got much of a refresh, I think, it should be a ST-EF41-7R brifter, it looks identical to me.
I know that a snapped cable would drop the RD on the small cogs since there is no cable pull and it would fully retract into the high limit, but mine was stuck in the largest cog. I thought I had to ride home in a high-cadence workout but when returning to the bike a few hours later, shifting worked as expected, again. Trying all gears on the rear on the way home I think I once or twice got a louder click, as if some kind of rachet was just about engaging, rather than the usual "satisfying"/full sound, but no further skipping and normal shifts all the way.
It is a commuter bike and ~7 years old, I must admit that it doesn't get as much love as my road bikes, so the cables and housings have been replaced 2-3 years ago last and it does get its fair share of rain on my commutes, I haven't opened the shifter to see if there is some rust or gunk buildup, yet. Cables move fine and at least the exposed parts look pretty ok, no fraying or rust.
My guess is that the problem lies in the shifter internals and I should note that I rode into quite cold weather (-5°C) out of the garage and into rain the day before, so I suspect this could be related. Could a cable get stuck from riding approximately 30 minutes in those conditions, could water freeze in the housings?
I did have the issue only once, any I idea what could be the problem, how to further diagnose or to fix it? Does something need greasing/cleaning? I have a good collection of lubricants from WD-40, chain sprays, grease and specific chain lubes at home...
I've found this question that gave me the hint about water in the cable housings:
How to prevent shifting issues due to derailleur or cables freezing in cold weather
Update
I have added two videos following Criggie's answer, put a bit of lubricant in the rear derailleur's pivots but it certainly wasn't stiff before.
There is a little audible scratch when moving the cable but in warm/dry conditions, it moves OK, so does the rear derailleur:
https://youtube.com/shorts/EPzHpNHdYCE
Shifting is OK, too... chain was degreased when it shot the video and I tweaked the cable tension afterwards a bit.
https://youtube.com/shorts/LVT-LM7M3N0
(Sorry, it is hard to film when you've only got two hands).
So, it was definitely a temporary issue somehow related to the outside conditions.