Jan 11 (Reuters) - The Baltic Exchange"s dry bulk sea freight index (.BADI) dropped to its lowest level since April 2021 on Tuesday, weighed down by weaker demand across all vessel segments. * The overall index, which factors in rates for capesize, panamax and supramax vessels, fell 126 points, or 5.5%, to 2,151, its lowest since April. 13. * The capesize index (.BACI) slipped 229 points, or about 9%, to 2,325. * Average daily earnings for capesizes, which transport 150,000-tonne cargoes such as iron ore and coal, dropped by $1,897 to $19,284. * Chinese stainless steel futures surged more than 5% on Tuesday, boosted by tight supply concerns as producers cut production. * "We expect dry bulk spot rates to soften seasonally in 1Q22 before returning to cyclical strength in 2022 as demand growth is expected across all dry bulk commodities," analysts at Jefferies wrote in a note dated Monday. * The panamax index (.BPNI) fell 134 points, or 4.7%, to 2,715. * Average daily earnings for panamaxes, which ferry 60,000-70,000 tonne coal or grain cargoes, fell by $1,210 to $24,435. * The supramax index (.BSIS) fell 43 points to its lowest level since April at 1,958.