global singleton gen_server

Dear all,
I'm trying to run an operation only once on cluster start but there's
clearly something that I'm missing in the global module (see other related
question here [1]).

Therefore this time I'm trying to have a single global gen_server which I
start directly from application start/2 callback with:
gen_server:start_link({global, ?MODULE}, ?MODULE, [], Options).

Nodes are already connected at that point (I can see them with nodes()),
however for some reason this registration works on all the nodes and I find
myself with multiple gen_server registered globally.

What is the proper way to register a global singleton gen_server at cluster
level on application start? mY need is to run an operation only _once_ a
cluster boots up.

[1] http://erlang.org/pipermail/erlang-questions/2021-December/101781.html