tailscale serve behaves unexpectedly with --set-path option

### What is the issue?

When I use the following command
```bash
sudo tailscale serve 127.0.0.1:8025
```
it works as expected and when I go to `https://node-name.tailnet-name.ts.net`, the page loads without any errors and I'm able to login and use the app.

However, if I add the --set-path option like this:
```bash
sudo tailscale serve --set-path /vaultwarden 127.0.0.1:8025
```
and then try to open `https://node-name.tailnet-name.ts.net/vaultwarden`, only part of the page is being displayed (the logo and loading icon), and when I check the Network tab in Developer Tools, I can see that some requests are being blocked with the errors `NS_ERROR_FILE_CORRUPTED` or`NS_ERROR_CORRUPTED_CONTENT`. The issue persist when trying different browsers and from multiple machines. If I remove --set-path option, it works again.

Any ideas on what might be the issue?

### Steps to reproduce

_No response_

### Are there any recent changes that introduced the issue?

_No response_

### OS

Linux

### OS version

Debian GNU/Linux 12 (bookworm)

### Tailscale version

1.66.4

### Other software

_No response_

### Bug report

_No response_