Flashing a new BIOS to a HP Compaq machine

Hello Techies.
Here is my machine (old but still lively):
HP Compaq 6000 Pro MT PC (64 bits), warranty expired, running Xubuntu 18.04.5 LTS (32 bits, because I made a mistake).
I can supply more details.
The actual BIOS is dated 2009, a 2015 version is available, but the manufacturer delivers it for Windows OS only, in .exe format.
It contains 21 files organised in one root and two directories, and I might have also detected the right one, its extension should be .bin.
I wonder whether the new BIOS my machine needs is among them...!
As far as I could understand, if I ran Windows I should just use an app to perform the update.
But since I don't, I have to do it manually.
(Actually I realised HP has a particular service called HPLIP for Linux machines, but it only offers drivers and for faxes, scanners and printers only.)
I guess manually flashing the BIOS means pressing setup key (F10) during POST and allowing the system to get the right file from a USB stick. One containing the BIOS only?
What I'm writing is just a 'more or less theory' I've collected reading up on it.
Would you please give me precise information about updating and a plain procedure to get it done, because I don't want to make my pc into a paperweight as I could read several times I run the risk of!
More: am I supposed to back up the old one? And how?
Can you help? Is there someone out there who's met the same issue?
I thank you very much.
Alberto