The alabaster.treese package implements methods for saving and loading TreeSummarizedExperiment objects under the alabaster framework. It provides a language-agnostic method for serializing the row/column trees, their links and the reference sequences, along with everything handled by alabaster.sce for the SingleCellExperiment parent class.
library(alabaster.treese)
tmp <- tempfile()
saveObject(tse, tmp)
roundtrip <- readObject(tmp)