Excess heat release (often referred to as "waste" heat), can be a noticeable contributor to urban heat islands, but globally it has two orders of magnitude less heating effect than greenhouse gas releases.
The critical factor is that greenhouse gases accumulate.
The effect of waste heat is discussed in the multiple Stack Exchange questions, e.g.
But let's work the rough numbers for a typical home heating requirement of about $10000$ kWh ($3.6$ GJ) per year. Since the Earth's total surface area
is $5.1\times 10^8\,\mathrm{km^2}$, this one home contributes about $2.2\,\mathrm{pW/m^2}$ ($2.2\times 10^{-12}\,\mathrm{W/m^2}$) of heat averaged over the Earth.
We now need to estimate our greenhouse gas emissions. According to the U.S. Energy Information Administration, 53 kilograms of $\mathrm{CO_2}$ are produced per million British Thermal Units (Btu) of natural gas heating. In SI units this is $5\times 10^{-8}$ kg/J, so over a year our home will produce about 1800 kg of $\mathrm{CO_2}$.
According to the IPCC, only about 44% of anthropogenic $\mathrm{CO_2}$ stays in the atmosphere, the rest being absorbed by the biosphere and oceans, so our house's $\mathrm{CO_2}$ contribution is reduced to 800 kg.
The radiative forcing for small additional amounts of atmospheric $\mathrm{CO_2}$ is
$$\Delta F = 5.35 \ln{\left(1+\frac{\Delta C}{C_0}\right)} \approx 5.35 \frac{\Delta C}{C_0}\, \mathrm{W/m^2}$$
where $C_0$ is the base $\mathrm{CO_2}$ concentration.
According to Wikipedia "Each part per million of $\mathrm{CO_2}$ in the atmosphere represents approximately 2.13 gigatonnes of carbon, or 7.82 gigatonnes of $\mathrm{CO_2}$."
The Earth's atmospheric $\mathrm{CO_2}$ concentration (as of May 2022 was $421$ ppm, giving $C_0=3.3\times 10^{15}\,\mathrm{kg}$ of $\mathrm{CO_2}$. So the radiative forcing due to $\mathrm{CO_2}$ releases from our home's heating over a year is about $1.3\times 10^{-12}\,\mathrm{W/m^2}$, i.e. $1.3\,\mathrm{pW/m^2}$.
So per year, the effect of waste heat ($2.2\,\mathrm{pW/m^2}$) is actually about twice the greenhouse contribution ($1.3\,\mathrm{pW/m^2}$), but the crucial fact is that waste heat is transient while the green house contribution cumulates. Increases in atmospheric carbon dioxide have lifetimes of hundreds of years, so this year's greenhouse effect is not caused just by this year's gas releases, but also last year's, and the year before that, and so on. After 10 years our home's integrated greenhouse effect will be $13\,\mathrm{pW/m^2}$, and after a hundred years it will be $130\,\mathrm{pW/m^2}$, but its waste heat will still only contribute $2.2\,\mathrm{pW/m^2}$.
This cumulative effect manifests globally.
Humanity's current annual energy consumption is about $5.8\times 10^{20}\,\mathrm{J}$, corresponding to an averaged heating effect over the Earth's surface of about $0.036\,\mathrm{W/m^2}$.
The total anthropogenic greenhouse radiative forcing due to carbon dioxide since 1750 is estimated to be about $2.17\,\mathrm{W/m^2}$, $60$ times greater.
