Why is the island of Java so populated?

In Clifford Geertz' classic volume Agricultural Involution: the Processes of Ecological Change in Indonesia (1963), the author argues that the Javanese form of wet rice cultivation has a very high potential to "absorb labor". While Geertz' view has been criticized – for an enlightening discussion see Wood (2020), Chapter 6 (preview available on Google Books) – it is a good starting point towards answering your question. Wood writes:

It is fundamental to Geertz's view that different agricultural systems have different capacities for labor absorption and involution. According to Geertz, wet rice farming as practiced in East and Southeast Asia probalby has the highest capacity to absorb labor of any form of traditional agriculture...

Wood, (2020).

Thus, the particular attributes of wet rice farming systems in the tropics and subtropics allow these systems to support, and indeed in the views of some authors demand, high population densities. High density, high intensity wet rice systems are found throughout south and southeastern Asia.

However, as other responders to this question remarked, the properties of the physical environment are also critical factors in the potential for a high density wet rice system. Growing season temperature and rainfall will influence potential productivity, but in tropical and temperate monsoon Asia, soil fertility is probably more important. So the best examples of high density rice systems are found not just in the young, fertile volcanic soils of Java, but also along the major river valleys and deltas of the region, e.g., Mekong, Red, Chao Phraya, Irrawaddy, Pearl, Yangtze, Ganges, and in the fertile but narrow volcanic valleys of Japan. As noted above, the other islands you mention:

Madagascar, Borneo, Sulawesi, Honshu (Japan), and Sri Lanka

are characterized by older and more complex geology with significantly less fertile soils, and in the case of Japan, substantial areas with cool to cold temperate climate where rice agriculture would have been limited to a single crop per year, if at all.

The most fundamental reason with respect to other parts of tropical Asia is the earlier adoption of wet rice cultivation in Java. Grigg points out that the only places in Asia that had greater population densities in the late 19th century were China and Japan. Wet rice is just an amazingly productive form of agriculture, especially by traditional standards, before the age of synthetic fertilizers.

Japan is a different case. It is only recently that Java's population has surpassed Japan's, and that is due to Japan having some of the lowest fertility rates in the world. Java is still at an earlier stage of its demographic transition, but over time its population growth is gradually slowing down.

One important factor is soil fertility:

Java’s soils are very fertile because of periodic enrichment by volcanic ash.

In contrast, with the two nearby large Indonesian islands of Borneo (shared with Brunei and Malaysia) and Sumatra:

Borneo, the world’s third largest island, has exemplary rainforest soils: shallow and nutrient poor. The abundance of rain in these ancient ecosystems has leached the soil for millions of years.

In contrast to overpopulated Java the neighbouring island of Sumatra still provides huge unused land reserves. However, by far not all of these reserves can be regarded as real agricultural potentials, e.g. for resettlement projects. Especially the poor soils often prove an agricultural handicap. Besides soil fertility the existing vegetation has to be considered. Thus, for example, the so called "alang alang grass savannas" in general show better potentialities than forest areas, while most of the swamps prove rather unsuitable for agricultural development.

(I don't think it makes sense to compare Java with islands like Honshu or Madagascar that are in other countries with entirely different histories.)