It appears you have copied the whole old /etc/config/dhcp file from 15.05. That will not work.
The configuration of dnsmasq has changed a lot. Discard the old file and edit the new one to add your extra interfaces. I think the new default file is at /rom/etc/config/dhcp. Copy that over the old one. If there isn't a default file in rom, remove the existing file and reboot so the firstboot script regenerates it.
Can I do it over the GUI? The problem is that I have no idea how to configure the /rom/etc/config/dhcp.
Basically I have 2 interfaces where I need to use DHCP:
Yes, but first I would start with a fresh image without restore of config.
Just go to the interface in the GUI and click on edit then you can configure the DHCP server individually for each Interface.
@faser makes a good point that trying to reuse any config file from 15.05 into 21.02 is likely to have problems. Use your old files as a reference but rebuild the configuration starting from the new defaults.
Looks like I managed to screw up my router... After a few sysupgrade commands it won't start any more, I can not even do a factory reset as it looks like I can not even connect via an ethernet cable to the router.
Thank God, I have another one I can use for now.
If you have any suggestion of what to do to start the old router, I would appreciate it. Thank you.