I have consulted to National Marrow Donor Program/Be The Match [0] off and on for several years. There are typing labs using long reads but most reporting/matching/analysis is still performed at the nomenclature level [1].
I hope in the near future we'll be able to simply assemble the entire MHC for each sample, as messy as it might be, see e.g., "A diploid assembly-based benchmark for variants in the major histocompatibility complex" [2].
[0] https://bethematch.org [1] https://www.ebi.ac.uk/ipd/imgt/hla [2] https://www.nature.com/articles/s41467-020-18564-9