Flickering problem and BIOS version question

[FN15]

Good morning:

I have had a "HP Pavilion Power - 15-cb031nl" notebook for 7 years:
I now have the BIOS version: "F.41" from 01/12/2020,
and I have Windows 11 25H2 (I upgraded to Windows 11 only a month ago).

1.

The app: "HP PC Hardware Diagnostics Windows" (version 2.9.0.0, downloaded a few days ago from the official HP website), tells me that there is a better version of my current BIOS (F41), namely F.16;
furthermore, over the course of 7 years, I must have updated the BIOS (from the official HP website) at least 2 or 3 other times (I don't remember exactly how many times).

2.

I also have a problem with my screen, for many years now (I think at least 2 or 3 years, if not more), and that is that at a certain point in these 7 years, (I don't remember the exact moment) my HP monitor started to flicker: the flickering is also present when I access the BIOS menu (so I believe it is not a Windows problem).

This flickering only happens when I'm in "battery mode": to try to remove it, every time I use the PC I always have to repeatedly press "F2" and "F3" (which are the keys to increase and decrease the brightness from 10% to 100%), and, whenever it (i.e. my PC) wants, without any sense or reason or logic, at a certain brightness percentage (for example, today at 50%, tomorrow at 70%, the day after tomorrow at 90%), the flickering disappears, and I get the precise brightness value I had set (that is, in the previous examples, either 50, or 70, or 90%). Otherwise, if I don't do this operation (at 50, 70, or 90%), the screen always remains at minimum brightness (as if I were at 10%), and with a slight, or strong, flicker.
The moment I plug in the AC power cord, the flickering disappears, and the brightness becomes the same as what I had set with F2-F3 (e.g., 50, or 70, or 90).

Over the years, I have tried every possible option: for example, I looked at all the Windows power saving settings, I updated the drivers for my NVIDIA graphics card [from the official NVIDIA website], etc. etc.

But, recently I began to suspect that perhaps the problem might be the fact that, over the course of these 7 years, I should never have updated my BIOS, not even once, but instead left the BIOS version I had when I initially bought the PC: in fact, in the first few years that I used the PC, I never experienced this flickering or 10% brightness drop.

Furthermore, the "HP PC Hardware Diagnostics Windows" app simply tells me if I want to update from F.41 to F.16, without explaining whether F16 is the best and most updated version of the F.41 BIOS I have now:

and if I go to the official HP website and enter the brand and model of my PC, to find new drivers, I do not find the 25H2 version of Windows 11 (which I have now for a month), and if I try to enter the version: "Windows 24H2", or "Windows 11" without any specifics (e.g., without 23H2, 24H2, etc.), HP simply tells me that I have the most updated drivers, without telling me instead: "there is the F16 version of the BIOS which is better than the F41".

Furthermore, I have not found anything anywhere on the internet that shows me a "ranking" of the most updated BIOSes for my PC model: so I don't know if, by updating to F16, I risk freezing and ruining my PC completely, making it unusable.

Could you help me?
1. Do I need to update to F16?
2. How can I fix the flickering and brightness drop problem?

Thanks for anything you can answer.