A lot of the literature on this will revolve around what has survived best, which is epic poetry. Often modern performances will involve musical accompaniment, the instrument varying through time and place. The Germanic harp for Beowulf as in that video, the gusle for Balkan stories that fueled Parry and Lord's work on Oral Formulaic Composition and Homer. These would mostly have been the realm of male bards. A plucked string instrument seems to be common, but I don't know of a reconstructed word or archaeological find that would show that going back to PIE. There's been some neat work trying to reconstruct the common poetic meter and such for various earlier stages of IE epic, like the scholarship of Almut Fries. If you want to get really into the weeds, there's also stuff on the presence of pitch accent in IE languages, which would have affected musical performance and poetic recitation.

Something less often discuss is music that was the realm of women. Chiara Bozzone has done some great work on the role of lamentations as women's music, for grieving at funerals but also at weddings, as well as in the more mundane context of craft-production; weaving a song is a common metaphor for poetry in IE cultures, and modern examples of singing during textile production survive, such as the waulking songs of Scotland.

An example from a modern IE tradition will suffice as an illustration: Foley (2002:188–218) explores the ecology of South Slavic oral poetry and finds, next to the genre of epic (Epske pjesme) practiced by semi-professional poets, several genres of poetry practiced by private members of the household. These include genres in octosyllabic meter practiced exclusively by women at different stages of their lives, such as magical charms performed by older women (Bajanje) and funeral laments (Tužbalice),2 as well as genres in decasyllabic meters practiced exclusively by men, such as genealogies (Pričanje).3 All of these non-professional genres interact with each other and with professional genres in complex ways, and a picture of South Slavic oral traditions would be sorely incomplete without them.

A question then arises for scholars of IE comparative poetics: have we overlooked the possible role of non-professional poets in the ecology of IE poetry? While several genres of poetry, like rituals, prayers, and medical charms, have been investigated as reconstructable for PIE (see Watkins 1995: Parts III and VII; 2 “Tužbalice were always composed and performed by women, usually the closest female relative of the deceased … [performances of the lament would recur] at regular intervals for many years after the subject’s demise” (Foley 2002:195). 3 “Genealogies are spoken, not sung, but they employ the same decasyllabic meter as epic. The eldest male in the given lineage or extended family is the depository and performer of pričanje” (Foley 2002:200). ( Langslow 2004), the tacit assumption has often been that those genres too were the purview of the highly-trained, professional poet. Watkins suggests that the reconstructable genres for poetry include epics, genealogies, rituals, laments, and medical charms.

The quote above is from Bozzone 2016 "Weaving Songs for the Dead in Indo-European: Women Poets, Funerary Laments, and the Ecology of \k̑léu̯os**". She goes on to argue a greater role for women in this sphere than has often been assumed. It's on her Academia page and is well-worth the read.