Toolchain related to the version of the firmware?

Is the version of the toolchain related to the version of the firmware?
If it’s relevant, if it’s built using the 22.0.0 toolchain, can it be used with 22.0.0 or higher firmware?

best regards.

The general answers are “no” and “yes”.
It should be possible to install and use any SDK with any version of the Toolchain, however later versions of the Toolchain will have improvements and bug fixes so it is always recommended to use the latest version.
Note that the Toolchain version numbers are linear - there are no parallel LTS and feature releases like there are with the firmware, so the latest version of the Toolchain (currently 2024.0) is always the recommended one.