How is it possible to Update the GRUB file from grub-install (GRUB) 2.12-5ubuntu5.1 to fall back to Safe Graphics with all other options the same

Question

I noticed that GRUB for Ubuntu 24.10 version is (GRUB) 2.12-5ubuntu5.1 - maybe the kernel version is 5.1? If so, it might be possible to install drivers that cannot be installed using the 6.x kernel. I want to be able to use HTML ports on NVIDIA GT210 video cards, but so far I have not been able to load a suitable driver. My system configuration (without the card being installed) is as follows:

# System Details Report
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Report details

Date generated:                              2024-12-05 11:02:20

Hardware Information:

Hardware Model:                              ASUS All Series
Memory:                                      4.0 GiB
Processor:                                   Intel® Core™ i3-4170 × 4
Graphics:                                    Intel® HD Graphics 4400 (HSW GT2)
Disk Capacity:                               750.2 GB

Software Information:

Firmware Version:                            1103
OS Name:                                     Ubuntu 24.10
OS Build:                                    (null)
OS Type:                                     64-bit
GNOME Version:                               47
Windowing System:                            Wayland
Kernel Version:                              Linux 6.11.0-9-generic

This question has two parts:

1. How can an entry be added to boot that boots into safe-graphics, like the safe-graphics option that is GRUB, except everything else as normal?

2. Is is possible to install the nvidia drivers at the GRUB menu so that they persist into the Ubuntu 24.10 login?

Update: Regarding questions from oldfred:

I ran the requested (with the results following):

stephen@stephen-ThinkCentre-M91p:~$ sudo ubuntu-drivers devices | grep recommended
stephen@stephen-ThinkCentre-M91p:~$ sudo dkms status
stephen@stephen-ThinkCentre-M91p:~$ sudo lspci | grep NVIDIA
01:00.0 VGA compatible controller: NVIDIA Corporation GT218 [GeForce G210] (rev a2)
01:00.1 Audio device: NVIDIA Corporation High Definition Audio Controller (rev a1)
stephen@stephen-ThinkCentre-M91p:~$ lspci -v -s 01:00.0
01:00.0 VGA compatible controller: NVIDIA Corporation GT218 [GeForce G210] (rev a2) (prog-if 00 [VGA controller])
    Flags: bus master, fast devsel, latency 0, IRQ 28
    Memory at fa000000 (32-bit, non-prefetchable) [size=16M]
    Memory at c0000000 (64-bit, prefetchable) [size=256M]
    Memory at d0000000 (64-bit, prefetchable) [size=32M]
    I/O ports at e000 [size=128]
    Expansion ROM at 000c0000 [disabled] [size=128K]
    Capabilities: <access denied>
    Kernel driver in use: nouveau
    Kernel modules: nvidiafb, nouveau

These results show that the NVIDIA video card is definitely installed. There are even two kernel modules associated with it. but as far as I can tell, the driver is not installed properly. The kernel version is 6, and the linked reference has instructions for kernel versions 5 for installation of the headers, which are old instructions, not for the latest kernel. Also, there is some doubt a to the manufacturer's support for this card. Perhaps another party needs to (or has already) written suitable drivers. Or maybe just the module needs to be swapped.

Please note that for this test a different computer was used, as the first computer ended up somewhat broken from video card tests and is just running from the internal DVI port now. The new properties are:

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