Namaste Govind Ji,
By Veda here, I assume you are chiefly referring to the Samhita portion of the Veda rather than the subsidiary texts (Brahmanas/Aranyakas/Upanishads). The YouTube channel भारतबन्धुः USA has full recordings of the Rgveda Samhita (Shakala Shakha in Kerala Nambudiri Style - although they do not chant the Valakhilya hymns: Rgveda 8.49 - 8.59), Shukla Yajurveda Vajasaneyi Samhita (Kanva Shakha) as well as a partial completion of the Gana (song form) of the Samaveda Samhita (rare Ranayaniya Shakha)
https://www.youtube.com/@usa7645/playlists. Some Vedic rituals are also presented in one of their playlists. Please note different Veda Shakhas have differing contents, styles, tones, hand gestures and subsidiary texts. Many other rituals can be found on scattered videos across YouTube, including parts of Somayajnas such as the Pravargya and Atitratram.
http://vedamu.org/VedicChanting.aspx also has full chanting of Rgveda Samhita (Shakala Shakha in common South Indian style, non-Nambudiri), Krshna Yajurveda Samhita (Taittiriya Shakha), Krshna Yajurveda Samhita (rare Maitrayaniya Shakha), Shukla Yajurveda Samhita (Madhyandina Shakha partially up to Adhyaya 27 out of 40), Shukla Yajurveda (Kanva Shakha in full), Samaveda Samhita (Kauthuma Shakha in both Gana and Rcha forms), Samaveda Samhita (rare Ranayaniya Shakha in Gana form for all parts except Rahasya/Uhya Gana), Atharvaveda Samhita (Shaunaka Shakha) and Atharvaveda Samhita (rare Paippalada Shakha but without svaras). Madhyandina Samhita of Shukla Yajurveda is also available in full in this playlist
https://www.youtube.com/playlist?list=PLsm-XTWJfOqd3IVtNO37iqozCv5npY72x.
And yes, the government of India has undertaken a project to preserve Veda chanting:
https://vedicheritage.gov.in/ It is quite comprehensive and covers the above Shakhas and also has another form of Samaveda Samhita (rare Jaiminiya Shakha in Kerala style in both Rcha and Gana forms, except Uha Gana and Rahasya/Uhya Gana). There are some Shakhas which have preserved written/printed versions, but are extinct in oral tradition. These include Kathaka & partially Kapishthala Shakha (both of Krshna Yajurveda), and Ashvalayana Samhita (Rgveda). As you probably know, many Shakhas are also fully extinct. Also, the Rgveda's Khilani is a special issue
https://archive.org/details/in.ernet.dli.2015.326386/page/n987/mode/1up?view=theater : parts of it such as Lakshmi Sukta are commonly chanted, and this printed version exists, but other Suktas I do not think are chanted by any group anymore. Also, different numbers and types of Khila are found through various old manuscripts, and some Khilas are lost to time.
My response purposefully has not gone into chanting of Brahmanas/Aranyakas/Upanishads, because this is a more complex issue and only some of them are still chanted in traditional transmission, however printed versions of many of them exist.
Kind regards,