Apparently the EMF was a shot-down proposal of how to reform/expand the ESM. Alas the documentation I found is rather vague [at summary level] along the lines of:
The European Commission's proposal for transforming the intergovernmental European Stability Mechanism (ESM) into a European monetary fund (EMF) under EU law would provide it with wide-ranging tasks. The ESM was created at the height of the European sovereign debt crisis in order to provide financial assistance for governments that had lost, or were about to lose, access to financial markets. It was established outside the Community framework by an intergovernmental treaty and is a permanent rescue mechanism aimed at safeguarding the financial stability of the euro area. The proposal met with considerable opposition at Council level, as the Council wishes to maintain the ESM's intergovernmental character, and would expand its remit only slightly.
So I got it that the Council was not happy with delegating any of its functions/powers in this respect.
But who was supposed to make decisions in the EMF, e.g. how were countries supposed to be represented? And what kind of decisions was the EMF supposed to have in its remit?
(N.B. I found some political statements justifying the EMF proposal like Manfred Weber's
“The political picture behind that is that in the last euro zone crisis we asked for the IMF’s (International Monetary Fund) help. Barack Obama was the president then so partnership was possible. In future crises, which we can’t exclude happening, I as a European don’t want to be dependent on the White House.”
Alas that doesn't explain much how the EMF was supposed to work.)