Why Buddhists generally uses OM?

Its date is given as "8th to 6th century BCE" i.e. at least 100 years before Gautama.

Now "Om" is also used in Buddhism.

Is its use the same as in Hinduism?

No, we use this context for Catudhatu insight meditation.

If you recite the OM, do you (or not) think it is connected to a Super Consciousness as described in the Vedanta?

In Tipitaka, we realize there still be Sekkha (Stream-Enterer, etc) who still rebirth maximum at 7 times. And AnagamiBrahma in SuddhavasaArupabrahma is included in these 3 sekkha, too.

In LakkhanaSutta's commentary wrote that there are some AnnagamiBrahma from KassapaSambuddha time still alive. This Brahma tell Isi in Arayanta country about 32 characteristics of the Buddha to let Isi can notice when they meet the Buddha. So Isi from this country call themselves Brahmana (Brahma's son). And that's why the Buddha taught about AriyaSacca (the truth teaching by Ariya) in DhammajakkappavattanaSutta.

However, the commentary also commented that what brahma learned from AnagamiBrahma was already blurred when the time gone by to the Buddha time.

Another, we trust in truth (origins&effects) and there are some supernatural can be truth as well.

I am not sure about the use of OM in Buddhism, but it's usage in Buddism seems to present as early as 1st and 2nd Century CE with currently available evidence.

Here is extract from the book "Gotama Buddha: A Biography Based on the Most Reliable Texts, Vol. 1" by Hajime Nakamura. Page 51.

The more than forty terra-cotta seals found in the ruins of the monas¬tery on the east side of the stupa, however, do reveal some historical facts. The seals were not discovered in one spot but in various places, at depths between 1.05 and 1.55 meters beneath the surface at the monastery ruins. All are unsymmetrically round, about three centimeters in diame¬ter. Some were found, just as they had been placed, in a feretory in a bhikkhu's (monk's) quarters. The seals read, in three- to four-line inscrip¬tions in Brahmi characters dating from the first or second century, "Om! [Possession of] the Bhiksu Sangha of the Devaputra Monastery at Kapila¬vastu" and "[Possession of] the Bhiksu Sangha of Maha-Kapilavastu." Om is a sacred syllable used by the Indians; its use here reveals the influence of the Sanskrit revival, particularly remarkable after the second century. Devaputra means "son of the deity" or "son of heaven"; it is a title used in inscriptions by the Kusana kings (such as King Kaniska).

I wish there are more scholars like Hajime Nakamura who would study Buddhism & Hinduism with giving the due respect they deserved and also be open about the influence of each on other.

Not Om, but Mu is used in most derivative forms of Rinzai zen. One simply says the word "mu", holding the vowel sound, for the duration of the breath. The resultant phenomenology is virtually identical. The only real difference is how the resultant state is viewed and leveraged for the purposes of further practice. Was it inspired by Vedic practice? Who knows. But there are only so many good ideas in the world. Eventually you're going to have some duplication.

ॐ is from संस्कृतम् Sanskrit, which was likely written in some form from c.1500BC & earlier; it was used, or whats sometimes called a preVedic form, before The Mahabharata & RigVeda, c. 800BC or so. There were & are various styles of it and its the basis in more & lesser part for many languages in the world. Some scholars would consider some languages to be Varieties of Sanskrit cf entirely separate languages. Sanskrit has lots of verb forms etc & is very excellent for reading Buddhist literature, in part because thats how much of the literature was originally spoken & written(or Sanskrit 'Variants' etc), and texts have various meters & sounds, & there are terms very excellent for nuances of existential meanings and a few characters fairly specific for Buddhism Texts.

The sounds are very significant aspects of spoken Sanskrit Language:

ॐ is The Universal Sound. This concept predates The Vedas as well as the time of Buddha Gautama! There are hundreds of Branches of Hinduisms & Branches of Buddhisms, and there are various Doctrines etc. Some, eg, say The Sound while in contemplation.

ॐ

Since the Chandogya Upanishad was written a few hundred years before Gautama Buddha, there's no doubt that OM is older than the Buddha. It doesn't matter whether it's a hundred years older or a thousand years older.

As far as I know, OM does not appear anywhere in the Pali suttas or the other Early Buddhist Texts. Also, Gautama Buddha himself had never used or mentioned OM, to the best of my knowledge.

In the Theravada tradition, phrases of homage to the Buddha like "namo tassa bhagavato arahato samma sambuddhassa" do not start with OM.

So, where is OM used in Buddhism?

It appears to be used mainly in Vajrayana or Tibetan Buddhism - the most famous one being "OM Mani Padme Hum". There are others like "OM Tare Tuttare Ture Soha".

So, where does "OM Mani Padme Hum" come from?

The wikipedia page on "Kāraṇḍavyūha Sūtra" states:

The Karandavyuha Sutra is a Mantrayāna sutra that was compiled at the end of the 4th century or beginning of the 5th century CE. According to the Kāraṇḍavyūha Sūtra, the sun and moon are said to be born from Avalokiteśvara's eyes, Shiva from his brow, Brahma from his shoulders, Narayana from his heart, Sarasvati from his teeth, the winds from his mouth, the earth from his feet and the sky from his stomach.

The sutra introduces the Buddhist mantra, Om Manipadme Hum, which it states can lead to liberation (moksha) and eventual Buddhahood. A. Studholme sees this famous mantra as being a declarative aspiration, possibly meaning 'I in the jewel-lotus', with the jewel-lotus being a reference to birth in the lotus made of jewels in the Buddhist Paradise, Sukhavati, of Buddha Amitabha. The mantra is the very heart of Avalokitesvara (the supreme Buddha of Compassion) and can usher in Awakening.

So, "OM Mani Padme Hum" appeared in Buddhism, through the Karandavyuha Sutra, which was compiled almost a thousand years after the passing of Gautama Buddha.

And, it's a mantra for the Bodhisattva Avalokiteśvara, from whom emanates the sun, the moon, Shiva, Brahma, Narayana, Sarasvati, winds, earth and sky.

Now, let's just make it clear that the Early Buddhist Texts and Gautama Buddha himself have never mentioned Avalokiteśvara, OM, Shiva, Narayana or Sarasvati. This is to the best of my knowledge.

What does OM mean in Buddhism?

The 14th Dalai Lama gave a lecture on the meaning of: OM MANI PADME HUM. He said:

It is very good to recite the mantra OM MANI PADME HUM, but while you are doing it, you should be thinking on its meaning, for the meaning of the six syllables is great and vast. The first, OM, is composed of three pure letters, A, U, and M. These symbolize the practitioner's impure body, speech, and mind; they also symbolize the pure exalted body, speech and mind of a Buddha.

The OP asked:

OP: Is its use the same as in Hinduism? If you recite the OM, do you (or not) think it is connected to a Super Consciousness as described in the Vedanta?

So, the answer is that OM in Buddhism has nothing to do with Super Consciousness or Vedanta. Rather, this is what it means in (Vajrayana or Tibetan) Buddhism: "These symbolize the practitioner's impure body, speech, and mind; they also symbolize the pure exalted body, speech and mind of a Buddha."

OP: Is it difficult to describe the philosophical basis, if the practice is somehow derived from concepts and knowledge from a text whose date is from before Gautama?

Mmm... not really. The Dalai Lama has explained the philosophical basis above.