How to handle dev server base behind a nginx inner sub directory

[IamIpanda]

I have a dev code-server with prefix a/b, nginx like that:

location /a/b/ {
    proxy_set_header Host            $host;
    proxy_set_header Upgrade         $http_upgrade;
    proxy_set_header Connection      upgrade;
    proxy_set_header Accept-Encoding gzip;
    proxy_redirect http://$host https://$host/a/b;
    proxy_buffering off;
    proxy_pass http://<ip>:8080/;
}

Now I enable port forwading on that code server to forward dev server 5173, finally I get a url like that:
https://HOST/a/b/proxy/5173/

Now it asking for
https://HOST/@vite/client.
Obviously it don't exist. How can I make that correctly point to https://HOST/a/b/proxy/5173/@vite/client?
I have multiple dev server on that HOST so I don't want configure it directly on nginx.

Current vite.config.ts:

import { defineConfig } from 'vite'
import preact from '@preact/preset-vite'

export default defineConfig({
  plugins: [preact()],
  server: {
    host: "0.0.0.0",
    allowedHosts: ["HOST"]
  },
  base: "./"
})

I tried several settings for base and it seems the vite cannot correctly realize the nginx prefix a/b.