The behavior you're seeing in the Virtual Network Editor typically occurs when Workstation loads the configuration without full administrative privileges. Even if the elevated configuration is set to Bridged, it often shows "Custom (Host-only)" in the main VNE window. Therefore, the discrepancy you're observing is primarily a UI refresh issue rather than the bridged mappings being disregarded.
However, it's important to take a step back and determine what you truly need within the VM. Bridging four physical network interface controllers (NICs) sounds logical if you expect the VM to act like a device directly connected to four separate physical networks. However, if you only need the VM to communicate between its interfaces, VMware’s NAT mode provides that functionality without requiring individual physical adapters.
NAT in workstation can map multiple virtual NICs to the same outbound path while maintaining full connectivity within the VM. Unless the VM needs to appear as four distinct hosts on the physical network, NAT may provide the same result with a much simpler configuration.
If you want a clear technical overview of how NAT works, theses references explains the logic cleanly:
https://pingmynetwork.com/network/ccna-200-301/nat-overload-cisco
(just general networking info)
If the VM requires true L2 adjacency with four external networks, then "Bridged" is the correct setting. In that case, the usual fix is to run vmnetcfg as an administrator and recreate VMnet2–5.
But if the goal is mainly connectivity, NAT is lighter, more stable, and avoids these VNE quirks.