Trick question: NO
Active ISP: Yes
I think that's "Maybe" at this stage, as there may be a provisioning fault. Anyway, which ISP?
PPPoE: Yes
What would you suggest as an PPPoE client?
Windows, macOS both have built-in PPPoE clients. Linux almost certainly too (I don't have a Linux desktop to hand to test with)
Testing this way does give you some additional clues. Using Wireshark or tcpdump on the ethernet link, you can see whether your PPPoE discover (PADI) packets are being sent, and whether any responses are coming back (PADO). Nice overview
here. Then if PPPoE is established, you'll be able to see if the PPP session itself establishes, and if not, what the problem is (e.g. bad username/password).
However, unless you've successfully configured this to work with the specific ISP previously - including the correct VLAN tagging if required - then *not* getting a PADO response doesn't necessarily mean a problem with the ISP.
Router is ZYXEL VNG8623-TSOB V5.50 (ABPM.5)C0
Is this an ISP-supplied and pre-configured router, or one that you have provided yourself?
If it's supplied and pre-configured, then another approach is to put a managed switch between the router WAN port and the ONT, and configure a mirror port on the switch to send a copy of all WAN->ONT and ONT->WAN packets. Then you stick a laptop running wireshark or tcpdump on that port, so you can see the packets being sent and received.
However, in this situation, the fact that the link doesn't come up by itself is good enough to raise as a fault to the ISP. You may have a green light, but either Openreach or the ISP may not have correctly configured the traffic path.