This does not look like a simple file deployment problem.
vfpext.sys is not a standalone kernel driver service that you can normally query with Get-Service vfpext. The Virtual Filtering Platform (VFP) extension is part of the Hyper-V virtual switch networking stack and is typically bound through Hyper-V networking components rather than exposed as a conventional Windows service. Therefore, Get-Service vfpext returning "service not found" is not, by itself, evidence of a broken Hyper-V installation.
The more important detail is that you are running Windows 10 Pro build 10.0.26200.8655 while the WinSxS payload you found belongs to the 26100 component baseline. A successful DISM /RestoreHealth and sfc /scannow indicate that the component store is considered healthy and Windows does not currently believe vfpext.sys should be materialized in C:\Windows\System32\drivers. In modern Windows builds, not every binary present in WinSxS is deployed to the live driver directory unless the corresponding component, driver package, or network binding is actually staged and installed.
The first thing I would check is whether the Hyper-V Virtual Switch Extension is registered at all:
Get-VMSwitchExtension
Get-VMSwitchExtension -VMSwitchName *
and whether the driver package exists in the driver store:
pnputil /enum-drivers | findstr /i vfp
If VFP is absent from both, this points to a servicing/package registration issue rather than a missing file copy operation.
Because HNS and vmcompute are running normally, this is unlikely to be a general Hyper-V failure. It may instead be an application assumption that vfpext.sys must physically exist in System32\drivers, which is not guaranteed on newer builds. Before attempting manual file copies from WinSxS (not recommended), I would collect Get-VMSwitchExtension, pnputil /enum-drivers, and Get-ComputerInfo | Select WindowsVersion, OsBuildNumber output to determine whether the VFP component is actually installed or whether the third-party application is performing an outdated detection check.