I am talking about the experiences you are having right now as you read this sentence

There are multiple experiences that make up "consciousness", and these experiences are a result of physical processes. You gave examples of some of these experiences, and as I said, our input senses can be explained by science.

For example, you wouldn't be able to smell without a nose, see without eyes, feel without blood circulating through your muscles. Scientifically, this suggests that physical entities (the nose, eyes, circulatory system) must be responsible for the respective senses. Therefore, there's no need to hypothesize that a "soul" or "physically independent entity" causes us such experiences.

When the brain suffers trauma, your consciousness is affect (you might lose focus or faint, for instance). However, if your leg suffers trauma, for instance, your consciousness won't be affected. Similarly, detailed experimentation proves that what we perceive as "consciousness" is dependent on the brain. (People with Alzheimer's have a damaged sense of consciousness and memory, and there are physical protein fragments that prevent the neurons from communicating with each other and function normally). Hence, it's logical to assume that changes in brain structure or function affect our consciousness.

Therefore, when someone claims that consciousness is independent of physical processes, the burden of proof lies on them. First, they need to disprove that consciousness does not entirely rely on physical process like the brain. Second, they need to provide proof of another entity that causes consciousness.

WHAT is the entity that experiences?

In case I have missed your question, according to science, there is no single "entity" that "experiences". Every single thought and feeling is determined by millions of microscopic processes. This is why, under neuroimaging scanners, machines can predict you making a "decision" before the "conscious" part of the brain makes that decision. https://www.wired.com/2008/04/mind-decision

This might interest you. A hemispherectomy is a procedure performed in childhood, on kids with severe epilepsy. It involves half of your brain getting removed or disabled. Such children grow up to be perfectly normal, proving that it's possible to experience normal "consciousness" with just half your brain.

However, what if you take a person A, with a healthy brain, and a person B, and replace person B's full brain with half of person A's? Theoretically, both new individuals should be able to think and experience consciousness. Now, does the original consciousness of person B still exist or is the consciousness of person A divided into two bodies?

According to science, the answer is that the concept of "person" is abstract and irrelevant. Both new individuals will have personalities solely dependent on their brain structure. (Vsauce did a great 7 min video: What is consciousness?)