Managed to make both work but I have issues with both:
1- eglot is slow when dealing with out-of-file declarations that have been included or imported.
2- lsp-julia’s indexing takes ages and apparently I have to do it every time I update my install. It’s also not light on the CPU in normal workload.
It appears the thing I need to really change is my CPU in all this. Thanks @Satvik !