This isn’t Shoegaze so much as Chillwave, but it’s Shoegaze adjacent and reminiscent of something like Mallory: Charlotte Hatherley covering Peter Schickele’s “Rejoice in the Sun” from the soundtrack to Silent Running.
For comparison, here’s the original from the closing credits:
Silent Running is still tree-hugging space hippie bullshit, and I’ve always found something off-putting Joan Baez’s voice (maybe the excessive vibrato?), but I’ve got a soft spot for this song.