Insert query performance

Hello All,

In a version 15.4 postgres database, Is it possible that , if we have two
big range partition tables with foreign key relationships between them,
insert into the child table can cause slowness if we don't have foreign key
index present in the child table? Basically it need to make sure the new
row already added to parent partition table or not.

And if there is any possible way(example query tracing etc) to get the
underlying system queries which gets triggered as part of the main insert
query? For example in above scenario, postgres must be executing some query
to check if the incoming row to the child table already exists in the
parent table or not?

Regards

Sud