Nice catch, trendy.
So I changed the network of the interface lan_temp to something completely different. It was conflicting because it was in the same subnet.
Now:
root@router-5:~# tcpdump -i any -vn '(host 192.168.0.254 and port 80) or ( host 192.168.3.1 and port 8088) or port 9002 or port 9001'
tcpdump: data link type LINUX_SLL2
tcpdump: listening on any, link-type LINUX_SLL2 (Linux cooked v2), snapshot length 262144 bytes
12:03:26.398348 tailscale0 In IP (tos 0x0, ttl 128, id 27464, offset 0, flags [DF], proto TCP (6), length 52)
100.103.232.85.58975 > 10.1.5.1.9002: Flags [S], cksum 0x5d54 (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:26.398624 veth2 Out IP (tos 0x0, ttl 127, id 27464, offset 0, flags [DF], proto TCP (6), length 52)
192.168.0.1.58975 > 192.168.0.254.80: Flags [S], cksum 0x599d (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:26.398637 eth0 Out IP (tos 0x0, ttl 127, id 27464, offset 0, flags [DF], proto TCP (6), length 52)
192.168.0.1.58975 > 192.168.0.254.80: Flags [S], cksum 0x599d (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:26.399469 eth0 P IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:26.399478 veth2 In IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:26.399681 veth2 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:26.399690 eth0 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:27.405365 tailscale0 In IP (tos 0x0, ttl 128, id 27471, offset 0, flags [DF], proto TCP (6), length 52)
100.103.232.85.58975 > 10.1.5.1.9002: Flags [S], cksum 0x5d54 (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:27.405507 veth2 Out IP (tos 0x0, ttl 127, id 27471, offset 0, flags [DF], proto TCP (6), length 52)
192.168.0.1.58975 > 192.168.0.254.80: Flags [S], cksum 0x599d (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:27.405516 eth0 Out IP (tos 0x0, ttl 127, id 27471, offset 0, flags [DF], proto TCP (6), length 52)
192.168.0.1.58975 > 192.168.0.254.80: Flags [S], cksum 0x599d (correct), seq 499422122, win 64480, options [mss 1240,nop,wscale 8,nop,nop,sackOK], length 0
12:03:27.406333 eth0 P IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:27.406340 veth2 In IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:27.406565 veth2 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:27.406575 eth0 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:30.402056 eth0 P IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:30.402065 veth2 In IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:30.402240 veth2 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:30.402248 eth0 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:36.403523 eth0 P IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:36.403533 veth2 In IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto TCP (6), length 48)
192.168.0.254.80 > 192.168.0.1.58975: Flags [S.], cksum 0x3382 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:36.403741 veth2 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
12:03:36.403753 eth0 Out IP (tos 0x0, ttl 63, id 0, offset 0, flags [DF], proto TCP (6), length 48)
10.1.5.1.9002 > 100.103.232.85.58975: Flags [S.], cksum 0x3739 (correct), seq 3853203873, ack 499422123, win 5840, options [mss 1460,nop,wscale 1], length 0
So it's getting closer. Not sure why it's not working though.