Due to alleged conflict with my Filemaker Pro 19 app my IT consultant warns me not to install OS beyond my current Catalina version. Does installing this software update include stepping up to the next OS (11) system?

First of all, it appears FileMaker Pro 19 does run under the current MacOS operating system, MacOS Monterey.

https://support.claris.com/s/answerview?anum=000035761&language=en_US

Secondly, the software update to sync your iPhone will not affect the MacOS operating system.

Claris FileMaker Pro 19 was last updates in December 2021, but they do not make it clear if they support macOS after Catalina. You should not update to a newer OS unless you want to risk rendering Filemaker unusable. You can contact their support service and ask them if Filemaker will work on OS 11 here: Get support in our knowledge base (opens in a new window)