I think there’s something wrong with your setup. One of my machines has a br0 and a setup like yours. 10-enp5s0.network is the physical “WAN” interface:

root@host10:/etc/systemd/network# cat 10-enp5s0.network
[Match]
Name=enp5s0

[Network]
Bridge=br0 # -> note that we're just saying that enp5s0 belongs to the bridge, no IPs are assigned here.

root@host10:/etc/systemd/network# cat 11-br0.netdev
[NetDev]
Name=br0
Kind=bridge

root@host10:/etc/systemd/network# cat 11-br0.network
[Match]
Name=br0

[Network]
DHCP=yes # -> In my case I'm also requesting an IP for my host but this isn't required. If I set it to "no" it will also work.

Now, I have a profile for “bridged” containers:

root@host10:/etc/systemd/network# lxc profile show bridged
config:
 (...)
description: Bridged Networking Profile
devices:
  eth0:
    name: eth0
    nictype: bridged
    parent: br0
    type: nic
(...)

And one of my VMs with this profile:

root@host10:/etc/systemd/network# lxc config show havm
architecture: x86_64
config:
  image.description: HAVM
  image.os: Debian
(...)
profiles:
- bridged
(...)

Inside the VM the network is configured like this:

root@havm:~# cat /etc/systemd/network/10-eth0.network
[Match]
Name=eth0

[Link]
RequiredForOnline=yes

[Network]
DHCP=ipv4

Can you check if your config is done like this? If so it should work.