Short answer -> it is better to use a cache files (along with cache pull and cache push steps) to store such variables and then load them to envman, so they are available at each build step.
Long answer -> It seamed to me that envman should not only carry variables between workflow steps, but also save and restore variables between builds. It seemed like a better way rather then store variables in cache files.
I could not get a clear answer from @Roland-Bak (after giving full access to a workflow & waisting 2 weeks to discus the problem), but I have found a thread Save state between build where similar problem was described and offered solution was to keep variable in a cache file.
I still spent some time trying to save and restore envman variables file, but it turns out to be not a trivial task.
First I tried to init envman (envman init) to a working directory but that implied a restriction to add --path paramet to every envman command.
Then I tried to update ENVMAN_ENVSTORE_PATH variable and set it to a cached file and that worked, I did not have to add --path to every envman command, but I had to set this variable to every script step.
My last attempt was to push cache file to ENVMAN_ENVSTORE_PATH and copy it back to cache after workflow is completed. But it turned out that ENVMAN_ENVSTORE_PATH file was empty on the very last script step (probably envman clears it`s cache file on beginning or on the end of each step).
So I gave up and applied solution with keeping value in a file