but you seem to miss some of the points that I endeavored to explain.
You are correct that all planets will eventually come to a equilibrium temperature, but you mention only one way in which that equilibrium can be obtained.
Since you understand the laws of physics, you know that there are three ways that thermal energy can be transferred away from an object: They are conduction, convection and radiation.
Since we are considering the Earth that is floating in space and since no one has measured any conduction of heat between earth and space we can assume that it does not exist, that leaves the other two effects, namely radiation which you mentioned and the convection.
The word “convection” in this case also includes the word advection.
To illustrate the phenomenon, we could conduct an experiment. Suppose that we take two large Dewar flasks of the same size and place the same temperature and quantity of water into them, let’s say we fill them only to the level where one third of the volume is air, then we take two small quantities of solid material that are the same size and temperature but one is highly radioactive and the other is not, we drop one into one flask and the other in the other flask, after that, we take a vacuum pump and use it to continually evacuate both flasks of the remaining air/vapor in the flasks, the question then is: Will the water in one flask disappear faster than in the other? And if it does, then why does it happen?

My reasoning is that the flask with the radioactive material in it will empty faster than the other one.
The radioactive material imparts energy to its surroundings, as proven by nuclear power plants.

It may not be a perfect analogy but if you consider that the water in the flasks represent the Earth and its oceans and the vacuum surrounding the water represents space that surround the Earth, then what happens in the flasks can also happen to the Earth.