Hello @BobTheBuilder001
"Recently the Unicastagent list was fixed manually, and the vCenter says "vCenter state is authoritative"."
The first thing I would be suspicious of here is 'why' - generally if that is necessary then either there was some change causing an outage (e.g. someone changed vSAN-VLAN to one that didn't exist on vDS and nodes isolated and vCenter went down) or there was some issue which caused vCenter to remove some nodes unicastagent entries from some/all nodes (e.g. ESXi cert issue or vDS sync/entity state issue). If it is the former then there shouldn't be too much concern that vC will do the same thing again resulting in the same issue, but if it is the latter then you should get the root cause of that resolved before re-pushing configuration via 'Update ESXi configuration'.
"Furthermore, I learned that also if the settings are not matching with the vCenter settings in the worst-case scenario some nodes get isolated, and I have to fix it manually again, but the VMs and data will not lost or damaged. (Is that correct?)"
Correct, but note that you can and should avoid it breaking the unicastagent list(s) again, some cause of that are fixed in some vC versions but the 3 things I check before ever repushing list is 1. vSphere client shows all vmk that should be tagged for vsan-traffic as having the tag (e.g. conforms with the output of 'esxcli vsan network list' on the node) - if it doesn't then there is an issue with the vC vDS entries/entities, 2. vsanmgmtd is running on all nodes and 3. All host show valid and non-expired host certificate in the vSphere client.
Note as well that if 'esxcfg-advcfg -g /VSAN/IgnoreClusterMemberListupdates' is enabled on a node that applying 'Update ESXi configuration' won't do anything nor clear the health alert state as the nodes have been set to ignore any update/check/change.
"1) Since I can not use the "Upgrade ESXi configuration" in this HTML client version, is there any command that I can execute to do the same thing from CLI?"
No, not aware of any (RVC doesn't have such function and this pre-dates vSAN MOB).
"2) Is it safe to patch the vCenter up to 6.5U3 with this error present? (Then I can remediate the error because the vSAN related functions become available)"
It should be yes, you can enable /VSAN/IgnoreClusterMemberListupdates on all nodes to prevent any further node isolation in the interim, then disable that once you have the option in Skyline Health to 'Update ESXi configuration' and use that.
Any reason you are running on such old ESXi+vC build here? If for hardware/other reasons you are bound to 6.x then you should at the minimum update to latest 6.7 U3 build.