The only way I can think of to track usage of these executables would be to use "manual mapper" configuration settings. This will involve finding a way to configure appropriate registry entries on each client computer to identify the executable files to track usage for. Are you familiar with the "manual mapper" concept?

In case it helps, here is a table with some information about which processes can be metered for usage on Windows. I don't expect Firefox and Chrome would meet the requirements for any of the first 3 rows.

Process can be metered if its executable…

Notes

…was installed by a Windows Installer (MSI) package that was installed for all users

…is located under the installation directory identified for an application in the “local machine” 32-bit Add/Remove Programs registry settings

These registry settings appear under the HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\ Windows\CurrentVersion\Uninstall key.

…is located under the installation directory identified for an application in the “local machine” 64-bit Add/Remove Programs registry settings

This requires the FlexNet inventory agent version 14.2 (from release 2019 R2.2) or later.

These registry settings appear under the HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\ Windows\CurrentVersion\Uninstall key.

…is explicitly configured for metering in the application usage component’s “manual mapper” configuration settings