There are three powers in the middle east who want to "rule the middle east". They are Türkiye, there is Israel who wants to establish Greater Israel, and there is Iran who wants to establish Shia and Persian control over the middle east.
All three now sense an opportunity with the USA leaving the middle east.
Saudi is not a player or contender to lead the middle east, has never been and will never be. It economic power is only built on oil and on manufacturing, or services etc. It is therefore a fickle economic power.
The Makkah Defence Alliance pact is designed to stop both Iran and Israel dominating the middle east when the USA leaves, and the Makkah Defence Alliance gives Turkiye an advantage is re-shaping the middle east.
Iran and Israel see the Makkah Defence Alliance pact as an issue for their respective geo-political concerns and interests.
Therefore, Israel and Iran both are on the same side on this issue, as they both want to see the Makkah Defence Alliance pact fail immediately as it will restrict both their freedom of movement in the middle east. That is why it is being "tested" so hard now, and why both Türkiye are Pakistan are having to engage in Yemen, before the pact is fully up and running. Iran is forcing the issue in Yemen to try and destroy the pact on birth, ie try and make it still born..
The issue is not that Iran a pawn of the USA. The issue is that Iran wants to see the Makkah Defence Alliance fail and is trying to force it in that direction with Yemen. ( I am of the view that Saudi restarted the war in Yemen, but Iran took advantage of it for its own purposes ).
I see a different picture and different reasons for the war in the middle east right now.