Hi, you are welcome.
In answer to your first question, when an update updates the Recovery partition and modifies the WinRE image file, it may include third-party drivers that are currently enabled in the operating system, but this depends on the specific update and its design. The WinRE image file contains a basic set of drivers needed for system recovery, and if third-party drivers are required for recovery operations, they may be included in the updated image file. However, not all third-party drivers may be included, and some drivers may be disabled by default in WinRE. If specific third-party drivers need to be included in the WinRE image file, tools such as DISM can be used to add or remove them manually, but this requires technical knowledge and experience.
As for your second question, yes, there are tools available to create a WinRE image or a Recovery partition on a computer. One such tool is the Windows Assessment and Deployment Kit (ADK), which includes the Windows Preinstallation Environment (WinPE) and other tools for creating custom installation and recovery images. You can get it from the link: https://learn.microsoft.com/en-us/windows-hardware/get-started/adk-install
I hope this was helpful, let me know if you have further questions.