not sure if this is may an Restriction from "Active Backup".
if you say you could only backup online Vm's > that sounds strange. i don't know a Vmware permission restricting this. either snapshot is allowed or not.
Could you check that the Active Backup is able to resolve all Hosts and vCenter. as if there is something not reachable > getting also inaccessible Alerts.
Good to investigate some more detailed logs,.... as the gui not telling much.
Also may good to check how much concurrent tasks you have configured. not sure if Active Backup have kinda internally Session limits. As NFC for vCenter/Esxi have some limits. Vmware not restrict vms per Datastore to backup. me not aware of and doing backup of lot's vms.
Also good to check if you're at latest Patch Level > just to exclude some Past Bugs.
as it's using vddk > may worth to check as well which version of it it's using. as older vddk's have some bugs as well
You can follow 2 ways to backup a running VM.
1 + Make a clone using VMware vCenter (VCSA), and copy the new created files, with SHELL commands, as CP, (SHELL and SSH must be enabled),on a other place like your NAS (Synology).
In fact, I don't think, it's possible to copy the VMx and VMdk files, directly, without a clone.
2 + Use a Software, as VEEAM, to Backup or Replicate, the VM to a other place, as your NAS.urchase
It seems to be easy to do.
The VEEAM backup can be a separate Windows Server (maybe Linux ?), or a VM.
In the 2 cases, you must purchase licences (vcenter and/or veeam).
Just for information.... your Enterprise Plus also contains VMware VDP  (based on Avamar), so you own a VM Backup programm already. Now the bad news... with vSphere 6.5 the VDP goes EOA.
I never seen a VM Backupproduct which cant backup running VMs!! All products trigger a VM Snapshot so that the ESXi release the vmdk lock and the Backup product can read/backup the VMKDs. Most (all) Products use the VMware VDAP APU to get access to the data.
Veritas, ARCserve and countless others
I did configure Active Backup to work with free ESXi and backed up running VMs.
So you should check their documentation on how to configure exactly.
simply use veem bakup Recovery for backup of esxi along with vm.
About VEEAM, be careful if, after add VEEAM JOBS (backup and replication), you add a vCenter; all your jobs dedicated on VM or ESXi will failed.
You will have to redeclare all teh VM and ESXi inside each job.
There are many licensed solution available for backup and Recovery. However looking at your vSphere License Version, You do have VDP which you can use without paying anything additional. However you would require VDP appliance installed on vcenter to get this work done
VDP = vSphere Data Protection ??
No one should be recommending VDP at this point. The product is dead, EoL, and will not be supported for long. If you are going to implement some backup application, you need to choose something else.
Is it possible to add the vmware links about "VDP" ?
What does it mean ?
vSphere Data Protection