Shore Cord Failure - Please Help

how old is the cable ?
better replace the whole cable including the connectors

Note that you are choosing a quality industrial / marine cable

Impossible to say if the cord is the only culprit, but it's unlikely that there's anything wrong with the boat, imho.

Let's say your shore line (cord+plug) is rated for 50A.
If your onboard AC equipment demand more than that, either the dockside breaker should trip, if rated for 50A, or if it's bad (or rated for more), you should have also a breaker onboard, just behind the power cord, and by definition this MUST be rated for 50A.
So, the breaker(s) is(are) MUCH more likely to be the culprit(s), though it is indeed possible that the cord was a bit "tired" and after some time handling just shy of 50A (hence not tripping any breaker), it overheated and eventually melted.

The fact that you might have turned onboard equipment totalling more than 50A, or also the possibility that one faulty equipment might have absorbed more current that it should, is a bit academic.
In fact, also in this case, either one or the other breaker should have tripped anyway.

As a last though, you might also have NO onboard breaker at all, behind the shore cord.
I've seen boats without it, where the builder obviously trusted the pedestal breaker to protect the shore cord with no need for any other protection.
Should that be the case, I'd definitely recommend to take the opportunity to fit a shore cord breaker inside the boat.
These components can and do fail, and you don't want to rely just on something inside a dock pedestal, possibly old/never tested/corroded/whatever...

Well, it is possible that both breakers are stuck, but of course it's statistically much less likely than one at a time...
A new cord (plug included maybe, depending on whether it shows signs of wear/overheat) and a bit of monitoring sounds like the best plan to me.

If you've got an instrument onboard showing the total current absorption, you could also try to turn on as much stuff as necessary to reach and trespass the 50A threshold.
Any breaker working as intended should trip in a matter of a second or two, well before the cable can suffer any overheating damage.
Of course, if no breaker would trip, you should turn off PDQ whatever you are running, otherwise you could end with two melted cables rather than one! But this very simple test would tell you if the breakers are bad.

Very good practice indeed, if a bit annoying.
Talking of which, I recently had a chance to try a handheld thermal camera for an electrical panel inspection, and it works like a charm!
A check like the one you mention would only take a fraction of time, and without even touching the cable.
A good one is still a bit expensive, but it's now pretty high in my wish list for boat toys....

That's possibly true also of EU boats now, even if I'm not 100% sure.
The boats with no onboard breaker downstream of shorepower connection that I previously mentioned were all pretty old.

When you replace that cable on your reel, measure the distance from the plug to your damage spot and mark the new cable at the same general location. Once in place take a look and see if you have any impingement or other stress on the cable in that stored position. Given its location there's probably a better chance that somewhere this cable was pinched between the boat and dock or piling or perhaps a cleat, and a weak spot was encouraged to evolve into a failure.

It's happened to many of us.

That failure location looks suspiciously like an approximate length to exit a pedestal and wrap around a cleat on its way to the boat. Just a guess...

Check the lugs within your box to confirm the quality of those connections, any weakening, signs of heat or corrosion. If all is well, just replace the cable from the spool lugs out to your shore plug.

Great point on voltage at pedestal. Often overlooked. Your boat says you're drawing 30 amps, but low dockside voltage could mean a much higher draw at the plug. An old plug and cord is also going to drop some volts and increase amp load.

Thru the years, I have cut up many shore power cords that were found hot or already over heated.
Imagine any of the cables as a vacuum hose. Any nick, cut or opening for water to get in to, water WILL GET IN TO IT. Including the ends.
Once one drop of water gets in, it wicks up the whole conductor and the wire starts to deteriorate.
Any resistance that builds up, the conductor turns into a heating element.

Years ag0, one of my own cables, the end was dropped into the river for a second. No power was on the cable.
I draped the cable end over a hand rail, sprayed WD40 in and let it dry over night. Next day, all was fine,,, I thought.
One year later, that dark spiral line started to develop and I knew what it was. I dissected that cable and the black lead was wet & green the whole length.
Since then, I realized how fragile shore cables are.

When walking marina docks and I notice a cable wrapped in tape, I get a shudder down my back; Another heating element in the works.

https://www.toolup.com/Klein-CL800-...600A?msclkid=80b32bbb6e97126708884934a54edad0

The link above will take you to a pretty reasonably priced clamp on ammeter.
It does AC & DC in the clamp on mode and it's a nice all around tool to have.
With this you can see what the current draw of the boat is and set your mind at ease, maybe.