Welcome to the Community,
you can have multiple uplinks (vmnics) on the Management vSwitch, and connect them to different switches (as in your screenshot). In case the port on one switch goes down, ESXi will fail over to the other uplink. In case your physical switch supports this, you may even consider to configure Link State Tracking on the switches, to shutdown the ports to the hosts in case the uplink to the router is down.
Changing the Gateway IP address on the ESXi hosts' Management network settings cannot be done that easily (automatically). To archive high availability for this kind of setup, you'd rather want to configure HSRP (or somthing simlar to it) on the physical switches, or the firewalls.
Thank you for your response.
I would say that what I was trying to achieve is more on UPLINK HA for my ESX hosts.
Once again, thank you.