How does one practice Buddhism when experience is limited by the 6 senses?

In insight meditation, you are trying to understand the interrelatedness and interconnectedness between different parts of yourself, as well as yourself and the world. Not parts of the world with itself, that has no relations to you.

For e.g. the taste of the grape? how do you sense it? how do you perceive it? how does the concept of its flavour appear in your mind? what kind of emotions and memories does it invoke in you?

From this question:

On page 31 of Good Questions, Good Answers it says,

Explain what insight meditation is

During insight meditation a person just tries to be aware of whatever happens to them without thinking about it or reacting to it.

What is the purpose of that

Usually we react to our experience by liking or disliking it or by letting it trigger thoughts, daydreams or memories. All these reactions distort or obscure our experience so that we fail to understand it properly. By developing a non-reactive awareness we begin to see why we think, speak and act the way we do.

I don't think Buddhism does espouse interrelatedness and interconnectedness in such a way.

Your story of the origin of the grape isn't what I'd expect to be aware of when I eat a grape.

A story like that is useful sometimes for teaching that things have no independent existence: without sun, no grape; without seedling, no grape; without soil, no grape; and without this body and this moment and hunger, no experience of grape; etc. Therefore grape is precarious, impermanent, and shouldn't be relied on to be permanently satisfactory. I don't know how many of those stories (about different things) you need to tell yourself before you generalize it to the realization that everything is "conditioned".

Another way in which interconnected is used is in the sense of "no self". The Dalai Lama said he would be "imprisoning" himself, if he were to think of himself as "Buddhist, Dalai Lama, Nobel Prize Winner, etc." and that instead he prefers to think of himself as being "just like everyone else".

There is some other interconnectedness too, for example how you behave towards other people (e.g. whether you're kind or angry) allegedly has an effect on yourself (but I think that's an interconnectedness within you).

However in this answer I mention that Christopher Titmuss writes explicitly that the Buddha didn't teach that "oneness is the ultimate reality".

However, this source says,

In my fairly extensive reading of the Pali canon (not to mention Mahayana Sutras) I don’t recall the Buddha ever talking about our “separateness.” It’s a popular topic of discourse in modern Buddhist writing (I’ve written about it myself in Living as a River) but the Buddha just didn’t use that language (or if he did, it’s not been recorded). He talked a lot about misery, but he talked of the origins of misery lying in greed, hatred, and delusion. Now I know you can interpret greed, hatred, and delusion in terms of separateness (again, I’ve done so) but the point is that the Buddha didn’t use that language.

So if I say that "Buddhism doesn't espouse interrelatedness and interconnectedness" then perhaps I'm wrong: perhaps that is "a popular topic of discourse in modern Buddhist writing", even if "the Buddha didn’t use that language".

The Buddha taught about stress, the cause of stress, that there is an end to stress, the path to the ending of stress.

He taught the way by means of using the 6 senses to see the 3 characteristic of conditioned thing, dukkha (stress), anatta ( non-self), anicca (impermanent) using the five aggregates and the law of dependent origination.

Various other meditation practices, both insight and calm, are also taught to relieve attachments, hence suffering so that we are able to do the task of see the three characteristic in conditioned things.

When one of the three characteristics are seen clearly we pass through the gateway of voidness or emptiness ( when anatta is seen), the gateway of the signless ( when anicca is seen) and the gateway of the desirelessness ( when dukkha is seen). - Theravada tradition.

Thich Nhat Hanh teaches an eating meditation which is very similar to what you describe in terms of understanding interconnectedness. From his book "be free where you are":

When you eat you can practice mindfulness. Mindful eating can bring you a lot of joy and happiness. In my tradition, eating is a deep practice. First we sit in a stable position and look at the food. Then, mindfully, we smile at it. We see the food as an ambassador that has come to us from the sky and from the Earth. Looking at a string bean, I can see a cloud floating on it. I can see the rain and the sunshine. I realize that this string bean is a part of the Earth and the sky.

When I bite into the string bean, I am aware that this is a string bean that I have put into my mouth. There is nothing else in my mouth-not my sorrow or my fear. When I chew the string bean, I am just chewing a string bean-not my worries or my anger. I chew very carefully, with one hundred percent of myself. I feel a connection to the sky, the Earth, the farmers who grow the food, and the people who cook it. Eating like this, I feel that solidity, freedom, and joy are possible. The meal not only nourishes my body, but my soul, my consciousness, and my spirit. (pages 4 - 5)

It is interesting to note that Thich Nhat Hanh gave this dharma talk at a prison. (The recording of the dharma talk was later transcribed to a book.) He was speaking to people who had very little freedom in the conventional sense, but as always, his message is that with mindfulness we free ourselves from everything whether it be concrete walls, fears, hatred, anxiety and every moment should be a moment of meditation and mindfulness.

My understanding of this type of eating meditation would be not to think in a "busy" way about how a grape was grown, but to focus fully on the experience of eating the grape and understanding with gratitude all that has gone into the grape.

Here from Thich Nhat Hanh's Plum Village website is a bit about tea meditation:

At times, when we are drinking tea with a friend, we are not aware of the tea or even of our friend sitting there. Practicing tea meditation is to be truly present with our tea and our friends. We recognize that we can dwell happily in the present moment despite all of our sorrows and worries. We sit there relaxed without having to say anything. If we like, we may also share a song, a story or a dance.

If this particular style of teaching or practice is of interest to you, reading some of Thich Nhat Hanh's many books would be a good place to learn more. Best wishes.