Almost all of the electricity generated from gas in the UK is via CCGT, which is what you linked to earlier https://en.wikipedia.org/wiki/Combined_cycle_power_plantIf 49.9% is the figure, fair enough, but it seems high to me.
where the gas is burned to drive a turbine directly and then the heat from that is used to create steam which drives a steam turbine. 50%+ efficiency is typical for those.
Open cycle gas plant is rarely used. It's only advantage is it's cheap to build, but it's very expensive to run as a very large amount of the energy is wasted. It's the same gas turbine part and then all of the heat is thrown away.
Occasionally used when there is a shortage of generation and the high operating costs don't matter because the price of the electricity that can be sold is also very high.
Burning anything else such as coal, wood, oil, waste and so on is far less efficient, 20-30% typically, which is also why electricity from coal is both far more expensive and has a much higher CO2 output per kWh, as vast amounts of the energy is wasted.
For any modern heat pump heating system, just forget about S plan, on/off thermostats and the rest. It's irrelevant.
While it's possible to shoehorn a heat pump into a place where a gas boiler was, just doing that will result in a low performing, expensive to operate system. That will be most or all of the systems that you will hear complaints about.