A checklist of mosses of Hawaiʻi is here: https://www.researchgate.net/publication/237372043_A_revised_checklist_of_Hawaiian_mosses. A list of mosses of Hawaiʻi Volcanoes National Park by M. Waite in 2007 is here: https://core.ac.uk/download/pdf/10598018.pdf.
The California Native Plant Society publishes a journal, Fremontia, and the entire Volume 31, No.3, a special issue, is about bryophytes and has some interesting articles. There is a small charge for the issue: https://store.cnps.org/products/fremontia-vol-31-no-3.
Hawaiian stream algae have received little attention. One major study by A. Sherwood et al in 2014 is described in the paper The Hawaiian freshwater algae biodiversity survey (2009–2014): systematic and biogeographic trends with an emphasis on the macroalgae. The study looked at 1,786 habitats on six Hawaiʻi islands. One conclusion: “Forty-four well-characterized taxa were assessed for global distribution patterns. This analysis revealed no clear biogeographic affinities of the flora, with 27.3% characterized as “cosmopolitan”, 11.4% “endemic”, and 61.3% as intermediate. The paper can be accessed here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4222836/.