I don't find that to be the case with wg - have actually tested this and found a ~1-2% difference in battery consumption over a full charge, all on lte (pixel 8, graphene). Openvpn, though - yeah.
Definitely possible. Now I want to dig out a stock Android phone and retest. Aiui tailscale shouldn't introduce much if any load over wg, but I also wonder if you'd have different results with standalone wg.