I have a old PC that can't be upgraded to Windows 11 and I am thinking of installing Linux on it.
I haven't decided on a distribution (distro) and I am open to any recommendation.
My main questions are about performance and compatibility with the Logitech G27 steering wheel.

Should work fine in Proton or Wine. DXVK will probably provide greater performance but you may need to use WineD3D with your GPU if Vulkan isn't supported.

Lately a lot of strides have been made with wheel support in recent kernels with many DD wheels gaining kernel level support. Logitech wheels have been around forever and are well supported.

https://github.com/berarma/oversteer will be your friend there.

CPU/GPU should be fine for performance. New LFS graphics update might have issues as the DX requirement will increase and might require DXVK (and thus Vulkan support).

There used to be shadow/sound issues in Linux but there's an alternate shadow method in settings somewhere that should fix that if you encounter issues. Sound should be fine.

Thanks for the reply! My GPU supports Vulkan 1.3. I don't know much about Vulcan. But I think it should be able to run LFS after the graphics overhaul.

As mentioned above, Proton can be used to run LFS and is probably your best bet here.
I've been running LFS for years using proton. I can't say I've had any issues.

Quote from MorePain :

Is it possible to run LFS on I5-6400? .

On this processor and platform, you can also install Windows 11 24H2.

It is not a complicated 'operation'

Quote from Lucas McFly :

On this processor and platform, you can also install Windows 11 24H2.

It is not a complicated 'operation'

At one point Microsoft will break it. They already have caused boot BSODs on unsupported hardware without any way "back".

Plus if Linux works, why not?

I have been using Windows 11 on i7-4790K for 2 years and I have no problems with BSOD

Quote from Lucas McFly :

I have been using Windows 11 on i7-4790K for 2 years and I have no problems with BSOD

Yet.

Most Windows users nowadays tend to just use it because its mainstream and it just works.
You don't have to be a tech genius to find your way around windows.

Though for me - there are so many factors that pushed me to move away from it completely and be a full-time linux user.
1) Windows is paid
2) Paid and full of bloatware - this one is redicolous. Atleast offer a free version with bloatware and a clean paid version.
3) Data harvesting - They claim to not do such a thing. Personally i feel this was what they were trying to accomplish with Copilot on an OS-level. Being able to "require" the use of user data for Copilot, but then be selling the data on the side.
4) Multiple control panels
5) Then there are those other issues that has existed for years and is still to this day not confirmed to be patched. Its incredible. My win11 sim-pc got stuck in a boot loop a few months ago and at that point i seriously considered switching that over to Linux as well. Its insane to me that even after all these years they still have not been able to fix the well known boot loop.
6) Micro$oft bought Mojang (Company that made Minecraft) in 2014. A while after this, they got rid of the good old mojang login - where you'd just need a username and a password to log in. They got rid of the old login method completely, so you'd need to migrate to a Micro$oft account.

I could go on, but these are the biggest reasons for me.