Some VPS will manage your kernel for you and use a 'optimized' kernel. You can often change it to what you want. But sometimes you have to go into the control panel to change it.
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Possibly NixOS? It's all about having a reproducible OS based on a configuration file. I think with Nix flakes you could do exactly what you want on the OS level.
Though beware that it's kinda different to all the other Linux systems you might have tried.
If they're VMs, just install the kernel you want - keeping them updated is your responsibility anyways. If they're containers (Virtuozzo), you're not gonna change the kernel anyways.
You can export VM's and move them from provider to provider like that. How about switching everything to containers instead so the host OS does not matter?
It shouldn't be a problem.