I think it's currently non-selfhostable. You can host your own git server (knot) and CI runner (spindle) but not really the UI/API itself, but they're working on changing it. Currently it's a bit centralised
you can selfhost the appview: https://blog.tangled.org/bobbin, which makes all of tangled fully selfhostable now.
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It is self-hostable, but Tangled could disclose that great fact a bit more upfront.