The LAION project ( https://laion.ai/ ) is probably the closest thing to this.

They're looking for volunteers to help work on their fully F/OSS ChatGPT successor now. A video describing the help they need can be found here.

They have a great track record on similar scale projects. They've partnered with /r/datahoarders and volunteers on creation of training sets including their 5.8 billion image/text-pair dataset that they used to train a better version of CLIP.

Their actual training of models tends to be done on some of the larger European supercomputers, though. If I recall correctly, their CLIP-derivative was trained with time donated on JUWELS. Too hard to split up such jobs into average-laptop-sized tasks.