This is the update that nobody asked for but I shall put it here. In case one day someone has a similar question and finds it somehow.
I tested the second method and it works.
I used DNS leaks websites to test if the DNS was leaking and,
For the browser in the work profile, the DNS was the same location as the VPN IP because the DNS query was provided by the VPN.
For the browser in the personal profile, the DNS was provided by Rethink DNS because SOCKS5 proxy didn’t transmit it. But the IP was the one from the VPN in the work profile because it was transmitted through SOCKS5 proxy.
I hope this is understandable, sorry for my bad English. For there to be no discrepancy in DNS queries, use the browser from the work profile and not the browser from the personal profile.