Mahabharata seems to suggest caste-mixing was already happening:
"Bhishma said, 'The Brahmana, the Kshatriya, and the Vaisya are regarded as the three regenerate orders. To wed in these three orders has been ordained to be the duty of the Brahmana, O Yudhishthira. Through erroneous judgment or cupidity or lust, O scorcher of foes, a Brahmana takes a Sudra wife. Such a wife, however, he is not competent to take according to the scriptures. A Brahmana, by taking a Sudra woman to his bed, attains to a low end in the next world. He should, having done such an act, undergo expiation according to the rites laid down in the scriptures.
"Bhishma said, 'For the Kshatriya, O delighter of the Kurus, two wives have been ordained. The Kshatriya may take a third wife from the Sudra order. Such practice prevails, it is true, but it is not sanctioned by the scriptures
Does Manu-smriti mention how numerous mixed-caste people were from the standpoint of when it was written?
There is no scholarly consensus about its date - so if any information is available for any epoch in the range given below it would be acceptable.
Eighteenth-century philologists Sir William Jones and Karl Wilhelm Friedrich Schlegel assigned Manusmriti to the period of around 1250 BCE and 1000 BCE respectively, which from later linguistic developments is untenable due to the language of the text which must be dated later than the late Vedic texts such as the Upanishads which are themselves dated a few centuries later, around 500 BCE. Later scholarship, shifted the chronology of the text to between 200 BCE and 200 CE. Olivelle adds that numismatics evidence, and the mention of gold coins as a fine, suggest that text may date to the 2nd or 3rd century CE.
Most scholars consider the text a composite produced by many authors put together over a long period. Olivelle states that the various ancient and medieval Indian texts claim revisions and editions were derived from the original text with 100,000 verses and 1,080 chapters. However, the text version in modern use, according to Olivelle, is likely the work of a single author or a chairman with research assistants.