Multiple Subnets within ESXi host

As the comments already pointed out - you need a router.

You said that you already set your routes - where did you set them to? You cannot just set the routing to any IP device and hope that this will forward your requests. The target point of a set route must be any kind of device that knows what to do with packets they get - this need not be a "hardware router", it must be any kind of software that is capable of routing.

Theoretically it is even possible to make a Windows Client/Server a router - you just need to add interfaces in all the networks between which you want to route (what you already did, as far as I understand), and you need to install a software that will route the traffic - Windows Server for example has a role for this.

TL;DR: You want to route traffic between different networks? It is not enough to put a client in both networks, this client must be capable of routing - it must become a "router". It is possible to make a router out of a Windows Server. Should you do it? As some people say, "it is also possible to shoot yourself in the foot. Neither is a good idea". But this is my opinion.