Chinese HW-465abc 12V UPS Outputs 3.4V Unless Pressing Chip—Possible Causes and Fixes?

I have a small Chinese-made UPS.



Currently, I am using the version with a 12 V output, but it is behaving oddly: it typically outputs only about 3.4 V. However, if I press on the chip XR2981 in the center of the board (labeled “U4” on the picture), it temporarily outputs the correct 12 V.
I have already tried resoldering the contacts, but the issue persists.
Interestingly, I own two identical UPS units, and both exhibit the same defect. They have never been used and have been stored in their packaging for about a year.
Does anyone have an idea what might be causing this behavior, and how it could be resolved?

AI: Could you provide the exact brand and model number of the UPS units?
It is a no-name UPS. Just bought on AliExpress.
AI: When testing, what are you using as the input power source and what (if anything) is connected to the UPS output? Also, have you checked the battery condition or voltage?
Input was from a USB charger. The batteries' condition was good, but without them it exhibits the same behavior as described. It behaves the same with a small load and without any.

Try adding lead tin and remove that grey tin. It looks overheated. Re-solder from scratch.

I don't quite understand. Should I first add solder to the chip's pins and then remove it? There seems to be an acceptable amount of tin there now.
Re-soldering the entire chip might be an option, but only as a last resort.

The overheating suggestion doesn't seem to be realistic: mechanical action is what's important. Simply pressing with a finger to dissipate the heat doesn't help. You have to actually press. It looks like a bad contact on the board. But simply bending the board or pressing near the chip doesn't help either. You have to press specifically on the chip.