Energy is not only a property of matter. Photons have energy, no mass, and are not matter but in fact force carrier particles.

Anything that occupies space and has weight is matter. And yes, every matter exists in time.

Thanks for that link.

In plain terms, energy has gravity.

the simple forms of conservation you probably learned in school are not entirely accurate. you probably learned that neither energy not matter can be created or destroyed; whatever you do, the mass you begin with will be the same as the mass you end with, and the same is true, separately, for energy. that's not actually true; mass can be converted into energy, and vice versa. the correct form of conservation is that the combined mass-energy is constant. mass can be destroyed, but only if a proportional amount of energy is created. the coefficient of that proportionality is the square of the speed of light. that's what E=mc² means. that's how nuclear weapons work, and why they're so powerful. c² is obviously a pretty big value, so when a small amount of matter is destroyed, it creates a large amount of energy

similarly, energy can be converted into mass, but doing so makes it much "smaller." c² units of energy will become 1 unit of mass. and mass, of course, interacts with space-time

It does. The energy density of the em field will contribute to the stress-energy tensor that changes the metric of spacetime.

Though the force itself is irrelevant

you put the words in the same sentence, hence you have created a relation between the words.

So Spacetimeis one thing. It’s not time and space.

Energy is a property of matter- as represented by heat and light; and measured as the capacity to extract work.

Matter does have an influence on the spacetime surrounding it, but it’s not a direct link between energy (or mass) and spacetime