eclipse.jdt.ls Support for Kotlin

Question

I have a multi gradle project. There are both Java and Kotlin files the project. I've configured neovim to use eclipse.jdt.ls and nvim-jdtls. However, I cannot navigate normally to Kotlin files. This is because the Kotlin files are not in my jdtlds-workspace cache (I looked for the classpath of where they should be and they are not there).

Is there a solutions to use Java and Kotlin files in the same project in neovim? More importantly, does eclipse-jdt-ls even support Kotlin files? My guess is no, but I have not found explicit documentation one way or another.

Pasted is my ftplugin/java.lua configuration files:

local project_name = vim.fn.fnamemodify(vim.fn.getcwd(), ':p:h:t')
local workspace_dir = '/Users/josephclark/.cache/jdtls-workspace/' .. project_name

local capabilities = vim.lsp.protocol.make_client_capabilities()
capabilities = require('cmp_nvim_lsp').default_capabilities(capabilities)

local config = {
    cmd = {
        '/Library/Java/JavaVirtualMachines/temurin-17.jdk/Contents/Home/bin/java',
        "-Declipse.application=org.eclipse.jdt.ls.core.id1",
        "-Dosgi.bundles.defaultStartLevel=4",
        "-Declipse.product=org.eclipse.jdt.ls.core.product",
        "-Dlog.protocol=true",
        "-Dlog.level=ALL",
        '-javaagent:/Users/josephclark/.local/share/java/lombok.jar',
        "-Xms1g",
        "--add-modules=ALL-SYSTEM",
        "--add-opens",
        "java.base/java.util=ALL-UNNAMED",
        "--add-opens",
        "java.base/java.lang=ALL-UNNAMED",
        '-jar', '/Users/josephclark/.local/share/java/jdt-language-server-1.10.0-202204131925/plugins/org.eclipse.equinox.launcher_1.6.400.v20210924-0641.jar',
        '-configuration', '/Users/josephclark/.local/share/java/jdt-language-server-1.10.0-202204131925/config_mac/',
        '-data', workspace_dir
    },
    capabilities = capabilities
}
-- This starts a new client & server,
-- or attaches to an existing client & server depending on the `root_dir`.
require('jdtls').start_or_attach(config)

local opts = { noremap = true, silent = true }
vim.keymap.set('n', '<leader>e', vim.diagnostic.open_float, opts)
vim.keymap.set('n', '[d', vim.diagnostic.goto_prev, opts)
vim.keymap.set('n', ']d', vim.diagnostic.goto_next, opts)
vim.keymap.set('n', '<leader>q', vim.diagnostic.setloclist, opts)

vim.keymap.set('n', 'gD', vim.lsp.buf.declaration, opts)
vim.keymap.set('n', 'gd', vim.lsp.buf.definition, opts)
vim.keymap.set('n', 'gi', vim.lsp.buf.implementation, opts)
vim.keymap.set('n', 'K', vim.lsp.buf.hover, opts)
vim.keymap.set('n', '<C-k>', vim.lsp.buf.signature_help, opts)
--vim.keymap.set('n', '<leader>wa', vim.lsp.buf.add_workspace_folder, opts)
--vim.keymap.set('n', '<space>wr', vim.lsp.buf.remove_workspace_folder, opts)
vim.keymap.set('n', '<leader>wl', function()
    print(vim.inspect(vim.lsp.buf.list_workspace_folders()))
end, opts)
vim.keymap.set('n', '<leader>D', vim.lsp.buf.type_definition, opts)
vim.keymap.set('n', '<leader>rn', vim.lsp.buf.rename, opts)
vim.keymap.set('n', '<leader>ca', vim.lsp.buf.code_action, opts)
vim.keymap.set('n', 'gr', vim.lsp.buf.references, opts)
vim.keymap.set('n', '<leader>f', function() vim.lsp.buf.format { async = true } end, opts)

Thanks.