It may work but I don’t think it was the reason why it wasn’t working.
Simply you were trying to ping an ip within a vlan from outside of the vlan. You’re PC was not tagged therefore it was not on that network segment.
Bridging the 3 interfaces is literally putting a cable from one network to another so whilst you have achieved what you wanted to, it’s been done with misconfiguration.
Through the network manager you should be able to create a new interface, select VLAN, input the relevant VLAN ID and then you can choose DHCP client or static setup.
This will tag your computer from the outset so you will “only” see traffic inside your VLAN.