段階 and 手順: the current stage and an ordered procedure
Compare a plan at the testing stage with a procedure that specifies switching off power first, distinguishing progress from a changed sequence.
The current level of progress
段階, read だんかい, means a stage or level. 計画はまだ試験の段階です。 says that the plan is still at the testing stage.
次の段階へ進む前に、結果を確認します。 says that the result is checked before moving to the next stage. It does not report that the next stage has already been reached.
The order for performing a task
手順, read てじゅん, means a procedure or sequence of steps. 作業の手順を説明しました。 says that the work procedure was explained.
この手順では、先に電源を切ります。 says that power is to be switched off first under this procedure. It specifies an order for carrying out the work.
Progress and a changed procedure
段階は変わりませんが、手順を変更しました。 says that the stage is unchanged, but the procedure was changed. These are separate pieces of information.
手順を確認しました。 says that the procedure was checked. Completing all its steps or finishing the plan requires separate information.
Did the stage change too in 段階は変わりませんが、手順を変更しました。?
Show the answer and why
No. The stage is explicitly unchanged. What was changed was the work procedure.