For some idea on where progress is on the port, the Discord server has plenty of small development updates. Developer Lywx has mentioned that while the initial release will not support 60fps gameplay, it is being worked on and should come at a later date. When asked about custom textures, Lywx responded "If i manage to make it fully working, yes. Its not that hard, but its missing some things." It is also worth pointing out that, according to developer MelonSpeedruns, this project will not be compatible with previously-released texture packs, and that they will need to be ported to this system. However, Lywx has posted pictures showing working custom textures, including 4K textures, but it's unclear if they will be fully supported in the initial release.
If you'd like to dig deeper into the project, you can join the Ship of Harkinian Discord server. Or, you can wait until March 22 to see all the news in their Direct.
Ship of Harkinian Direct on YouTube