You tend not need to check ports for outgoing traffic (leaving your home network/homebase/etc)as they should all be allowed unless you are running some high end super secure network and hardware, 99% of normal home users do not need to do anything with outgoing traffic/ports, think of how many users have streaming services (Sky, Netflix, Freeview, etc), smart devices, consoles, other eufy users, none have needed to make adjusts to their routers/firewalls. If you want to really test and do not know which ports are required, remove/disable/power off any devices like PCs that you are paranoid about and disable the firewall and test your eufy. Once done re-enable the firewall, you will then have either found the issue or eliminated the firewall as the issue. Off course, this will be your decision and responsibility should you want to test this way.
The fact that it does work and it is a delay, does indicate that it should not be a firewall issue, unless again, you have some super expensive firewall do some funky weird packet monitoring routing shizzles.