please note that the ESXi Standard vSwitch cannot use LACP, thus you would need to use static LAGs (port sharing without LACP or possibly physical ports) to connect the ESXi servers via MLAG.
ESXi does not need to use a LAG for the vSwitch uplinks. If you use a load balancing mechanism that keeps all flows from one VM on one uplink (e.g. based on source MAC or based on source port [of the vSwitch]), you can connect different ESXi server uplinks active/active to different switches. The switches just need to be in the same layer 2 domain (same VLANs).
The Distributed vSwitch is needed to use LACP for ESXi uplinks (Enterprise+ license level). Load Based Teaming (LBT), preferred by many VMware admins, requires the Distributed vSwitch as well.