Laptop Dell2020 switches off

In September 2022, I had the problem that my laptop Dell2020 frequently switches itself off

Problem

Laptop Dell2020 suddenly switches itself off while operating
This started happening on a specific day (I think it was Friday Sep. 24) and immediately happened about three times that day

It doesn't seem to happen when the laptop is idling, or only using a terminal screen (withing Gnome)
It seems to happen especially when I'm using a second screen
A couple of days prior to this event, we had an electricity outage. The battery was emptied and hasn't charged since. At one moment, I started the laptop without battery, hoping that this would enable the battery again to charge. According to BIOS, the battery is still at 40% of capacity
BIOS reported that it doesn't recognise the charger (I'm using a replacement charger with some damage to the wiring)
BIOS frequently reports that it date and/or time hasn't been set. This might be an indication that there is something wrong with charging or the onboard battery.
I've checked syslog and dmesg, but that didn't help much - I haven't done it thoroughly though, and I don't really know how to extract meaningful information from system logs
On Tue. Sep. 27, I replaced the charger with an official Dell charger (might not be the same as that came with this laptop). Now the battery is finally charging

Event seems to happen mostly when using a secondary screen
When going through system logs, I had the impression that it suggested that there were problems in this area.

I have the feeling that it might have to do with persistent storage. In this case an SSD

Since replacing the charger, the battery finally charged, plus that this happened shortly after an outage after which the battery didn't charge anymore
This might explain why it happens when using a dual screen or when not idling: Under such conditions, the laptop may use more electricity

In the past, I had similar problems with CPUs getting too hot. In that case, it turned out that a fan was blocked by some debris
In this case, I can hear the fan
The problem seems too irregular to be related to this: It also happens at times when the computer has been on for just a short while.