The efficiency pump alone can consume between 35-90 watts. With 16 hours of operation per day, that amounts to between 55 and 140 € per year just in pump electricity cost difference.
My heat pump with 6.1kw, not modulating, has so far run a maximum of 3 heating cycles of 2-3 hours per day this winter. Yes, it has been mild so far, but that’s how it is in theory with continuously running heat pumps and pumps.
Some a***hole even advises against modulating heat pumps for these reasons, because continuously running circulation pumps counteract efficiency.
But these are peanuts and theories.
Outside the heating season, the circulation pump has even less to do, certainly not 16 hours.
And so 55 to 140 € will more likely become 10-30 € optimization potential.