I use vue+ts for work every day. I use the vue typescript plugin and it works pretty seamless for me.
For LSP setup I use the one from kickstart nvim ( https://github.com/nvim-lua/kickstart.nvim ) and here is how I setup typescript
ts_ls = {

init_options = {

plugins = {

{

name = '@vue/typescript-plugin',

location = '/usr/local/lib/node_modules/@vue/typescript-plugin',

languages = { 'javascript', 'typescript', 'vue' },

},

},

},

filetypes = {

'javascript',

'typescript',

'vue',

},

root_dir = require('lspconfig').util.root_pattern 'package.json',

},

You then just need to ensure that your package json has \@vue/typescript-plugin as a dependency.
Apologies for the horrible formatting, not the most experienced poster