Firstly, your photo is hard to see, but this looks like a standard HOUSEHOLD breaker. The markings look like a Siemens QP 1 pole breaker.
Where is this mounted?
These are NOT marine rated. What it should be is a marine panel like the one above with the reverse polarity indicator
The good news is your battery charger/converter DOES seem to be a high quality marine grade unit.
You posted "And I see now that there is no power flowing"
The meter on the charger should show some power flowing. You didn't mention how dead the batteries were and how you tested them. However, even a totally flat battery should, I imagine, be taking some power from that unit.
You have some investigating to do.
Based on the info you have posted, I would say the charger is not getting shore power. You found some breakers and that's good. As mentioned above, you want to first make sure the breaker on the dockside is on and you are, in fact, getting power into the boat somewhere. Are the outlets getting power?
So once you establish the boat is getting shore power, you will need to learn how this charger is connected to shore power. The previous owner may have hard wired it proper or simply added a power cord that needs to be in an outlet.
My first order of business would be to get that charger powered up because your description seems like it is not.
Looking at your photos of the battery terminals, there are several wires directly connected to them.
These (with the exception of the motor wire or the main cable to the A/B/ALL switch) MUST be fused close to the terminal. So that's a place to check also.
My boat does not have an A/B/All switch and my battery charger is directly (fused) connected to both batteries directly. It's likely your charger is wired this way too based on that photo.
Looking at your battery photo of the top battery, there are several wires connected to each battery. I would trace these and learn what they go to.
The heavy one with no plastic cover is probably going to your A/B/All switch. Then you have 2 red covered wires that look fairly heavy. One is probably the battery charger, the other...?? Then there is a thinner (blue) wire. What is that going to? Perhaps a low power device. Same on the negative terminal.
Once you are sure the charger is actually getting shore power, then you can troubleshoot further.
You can find the install and troubleshooting manual here
https://www.progressivedyn.com/marine-charger/