I get your situation, but unfortunately, Microsoft's strict hardware requirements for Windows 11, particularly regarding the processor, are non-negotiable. There isn't an official way to bypass these requirements. Your best bet might be to stick with Windows 10, which will continue to receive support and updates until October 14, 2025. That should give you more time to plan for possible hardware upgrades or replacements.
Doing anything with Windows out of scope is unofficial. You can't get any easier than clicking a checkbox to bypass while making your Windows USB install media which harms nothing in the long run. The restrictions are arbitrary because they want everybody to use TPM, has nothing to do with the actual CPU in your system.
That's because Intel's core CPU architecture didn't change for 5 generations. Sure a 13700k is going to be a ton faster in heavy applications because it's a whole 1.5+GHz faster but for regular stuff the older chips are 100% fine. I'm running a Dell Poweredge R830 with Xeon V4s (Broadwell 2014) that are 5th gen CPUs that has clients on it doing that regular stuff on a daily basis. If I added a cheap low pro GPU to the mix to offload H264 RDP compression to it their experience would be practically the same as their newer personal machines. The average desktop experience doesn't take a whole lot of power.
Mind you these are VMs restricted to 4 cores and 8GB of RAM with roaming profile images on a SATA SSD pool. One of my clients uses multiple monitors with a couple RDP sessions inside their own session daily.