[rush] `rush install --variant <variant-name>` doesn't work for the latest rush versions

[vhuseinova-msft]

Summary

The latest versions of rush (after 5.112.2) doesn't support variants anymore for rush install command even though an error (when running rush update) states that variants won't be supported in the next major release.

Repro steps

• open a monorepo with variants support
• install the latest version of rush
• try to run rush install --variant <variant-name>

Expected result: the variants ae supported until rush version 6

Actual result: the variants aren't supported anymore

Details

Standard questions

Please answer these questions to help us investigate your issue more quickly:

Question	Answer
@microsoft/rush globally installed version?	5.127.0
rushVersion from rush.json?	5.128.0
useWorkspaces from rush.json?	not specified
Operating system?	Mac
Would you consider contributing a PR?	No
Node.js version (node -v)?	v20.14.0