[Bug Report] <title>dae开启后无线连接正常，有线无法上网，怀疑dns问题

### Checks

- [x] I have searched the existing issues
- [x] I have read the documentation
- [x] Is it your first time sumbitting an issue

### Current Behavior

主路由jcg-q30-pro，immortalwrt，内核6.6.95
在有线的机器上nslookup无结果返回，无线的机器上一切正常，猜测可能lan口绑定的问题，我的配置如下
```
lan_interface: br-lan,wg0
wan_interface: auto
```
```
root@ImmortalWrt:~# ip a
1: lo: mtu 65536 qdisc noqueue state UNKNOWN qlen 1000
link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
inet 127.0.0.1/8 scope host lo
valid_lft forever preferred_lft forever
inet6 ::1/128 scope host
valid_lft forever preferred_lft forever
2: eth0: mtu 1500 qdisc mq state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
inet6 fe80::mac:518/64 scope link
valid_lft forever preferred_lft forever
3: wan@eth0: mtu 1500 qdisc noqueue state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
inet6 fe80::mac/64 scope link
valid_lft forever preferred_lft forever
4: lan1@eth0: mtu 1500 qdisc noqueue master br-lan state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
5: lan2@eth0: mtu 1500 qdisc noqueue master br-lan state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
6: lan3@eth0: mtu 1500 qdisc noqueue master br-lan state LOWERLAYERDOWN qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
7: ra0: mtu 1500 qdisc fq_codel master br-lan state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
8: br-lan: mtu 1500 qdisc noqueue state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
inet 192.168.11.1/24 brd 192.168.11.255 scope global br-lan
valid_lft forever preferred_lft forever
inet6 ip/64 scope global dynamic noprefixroute
valid_lft 246338sec preferred_lft 159938sec
inet6 fe80::mac/64 scope link
valid_lft forever preferred_lft forever
9: wg0: mtu 1400 qdisc noqueue state UNKNOWN qlen 1000
link/[65534]
inet 192.168.9.1/24 brd 192.168.9.255 scope global wg0
valid_lft forever preferred_lft forever
10: rax0: mtu 1500 qdisc fq_codel master br-lan state UNKNOWN qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
11: apcli0: mtu 1500 qdisc noop state DOWN qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
12: apclix0: mtu 1500 qdisc noop state DOWN qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
13: pppoe-wan: mtu 1492 qdisc fq_codel state UNKNOWN qlen 3
link/ppp
inet ip peer ip/32 scope global pppoe-wan
valid_lft forever preferred_lft forever
inet6 ip/64 scope global dynamic noprefixroute
valid_lft 258351sec preferred_lft 171951sec
inet6 fe80::mac/128 scope link flags 02
valid_lft forever preferred_lft forever
17: dae0@if16: mtu 1500 qdisc noqueue state UP qlen 1000
link/ether mac brd ff:ff:ff:ff:ff:ff
inet6 fe80::mac/128 scope link
valid_lft forever preferred_lft forever
inet6 fe80::mac/64 scope link
valid_lft forever preferred_lft forever
```

### Expected Behavior

_No response_

### Steps to Reproduce

我试过把br-lan改为eth0，lan1@eth0,lan2@eth0,lan3@eth0啥的也绑定过，但是还是没用。

### Environment

- **Dae version (use `dae --version`)**:
- **OS (e.g `cat /etc/os-release`)**:
- **Kernel (e.g. `uname -a`)**:
- **Others**:

### Anything else?

_No response_

Start by reproducing the wired-versus-wireless DNS failure with the reported ImmortalWrt 6.6.95 setup and inspect the lan_interface and wan_interface values, including br-lan and wg0 bindings. Collect the missing dae --version, OS, and kernel outputs, then compare behavior with the listed interface assignments; done means identifying a reproducible cause or documenting the exact configuration and diagnostics needed.

Written by the indexing model from the issue text.