Is it possible to add a menu entry at the bootloader for a new kernel?

hello,

I have fedora installed with kernel Linux 5.10.7-200.fc33.x86_64, which was working.
My hardware is Toshiba Qosmio laptop, with multi-boot.
This laptop has a NVIDIA video card 340. I had installed the offical driver from NVIDIA but at Fedora 32, this videocard gave me at an update issue's.

I found more or less a solution with https://www.if-not-true-then-false.c...nvidia-install, which is a patch for the kernel I believe. I have done some Fedora updates successfully. (In the meantime I have learned that this is maybe not the right way, patching everytime the kernel, or...)

Yesterday, I was updating Linux with "dnf update", and the packages are downloaded at /var/cache/... In this cache directory Fedora 34 was downloaded

There it goes wrong, my var disk is running out of space (4 Gb) and I could not patch the kernel anymore with NVIDIA driver. I think than I have made some mistakes by doing:

• dnf clean packages
• sudo pkcon refresh force -c -1

At least I had some space now again and I could patch the kernel but I had also done "dnf update" earlier as mentioned. So kernel version: kernel-5.12.8-300.fc34.x86_64 was downloaded and would be installed after the next reboot, which was failing: "Oeps seems something went wrong" (with dissapointed smiley).

Status now:

• The boatloader shows only kernel version: Linux 5.10.7-200.fc33.x86_64, so that I can only select this kernel (and Windows 10 (multi boot))
• I can still boot in text mode, runlevel 3. When the boatloader is shown, I press 'e' and add 3 after ... quiet"
• I have uninstalled Nvidia driver and activated nouveau driver again
• With rpm -qa kernel there two kernels: Linux 5.10.7-200.fc33.x86_64 and kernel-5.12.8-300.fc34.x86_64
• uname -mrs returns: Linux 5.10.7-200.fc33.x86_64

My Question:

• Can I repair this?
• Can I add an menu entry to the bootloader for kernel version "kernel-5.12.8-300.fc34.x86_64" and getting that one as the running kernel
• If so, I'm googling, but how exactly, so that I made not another mistake that runlevel 3 is also not working anymore!

I hope that someone can help me further