Plot hole or am I missing something?

I assumed he was cash-poor. Owning a shitload of land and a castle a thousand miles away doesn't necessarily help you pay the grocery bill this week.

Doctors are paid by their clients, and his is both poor and dead. He was stringing Maturin along by saying he had money, but he didn't. Maturin may be a spanish noble, but ten percent of the spanish society are nobles. Often that means little more than certain legal rights, not more money. we also see that his mother's family's castle is half a ruin.

This isn't a plot hole, it is an element of Stephen's character development and his backstory. Immediately prior to the events of Master and Commander he had fled Ireland after the failed rising, in a rush in order to avoid informers. As others have said, he did have land but it didn't generate cash flow and it is only later in the series he gains wealth. Hence after his patient died and his estate was unable to pay, he was marooned.

Mahon is in Mallorca, Majorca or Minorca(not sure which or correct spelling), an island in any event. Stephen is separated from whatever little bit he has on the mainland. It takes a while for a letter to get to anyone that can help, provided there is such a person. Stephen meanwhile is out of money. I think the phrase he uses is “he is separated from his little patrimony.” This may be because of the war or simply because he’s stuck in Mahon. His castle seems to. E a ruin so maybe there’s not much money there. And, spoiler alert, His uncle is evidently the one with all the money. And I’m not sure being a doctor meant wealth back then, and if it did Stephen is still young and maybe not established enough to be making real money yet.

TL;DR I think Stephen is really very poor at the moment, not a plot hole.

I figured it was due to his patient recently dying and possibly due to Mahon being in British hands while most of his funds were in enemy (Spanish) territory. I'm also willing to concede that POB possibly hadn't fully fleshed out Stephen's backstory at that point.

He was not brought up in the area. His Spanish roots are in Catalan, and Port Mahon is on the island of Menorca. Steven had come to Port Mahon with the promise of a job (rich patient I believe), but the job fell through, leaving him unemployed with no prospects.

In addition to the correct answers from others i'd like to say that i'm sure he didn't have a castle or loads of cash until his Catalan uncle/God father died and he inherited?

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I could be incorrect though.

If you're hunting plot holes in Aubrey/Maturin, you've come to the wrong shop, brother.

He wasn't from the area. He was from mainland Catalonia. Menorca was a British possession, and had been since 1708. When they take on water later in the book and Stephen goes ashore, he blends in, knows everyone and learns about the Cacafuego. Stephen's contacts later in HMS Surprise are through the Catalonian nationalists and in the first book they would have been working against the British, unlikely to trust someone willing to become a British officer.

His castle is in Spain, as we see in Post-Captain, is a ruin, and he tells Mrs Williams the rents are literal rackrents, as in, he would need to torture the tenants to get them to pay.

Having a castle doesn't make you rich, necessarily. If land doesn't produce anything then it can actually be a burden more than a boon.

Also, keep in mind this is before Stephen inherits the vast wealth, and also before he is really an intel agent (if one at all). He doesn't get paid for that anyways, remember.

Also, it was significantly harder to "pull out" money from a bank back then, and with the war, and the relative isolation of Mahon you have a larger problem.

It's also part of stephens characters, he just doesn't care or think about money and it makes sense he would just go off with this patient (who is now dead) without thinking about future funds.

The ability to subsist on credit is likely the only reason he didn't starve!

You obviously haven’t heard of the PayPal blackout in 1800? It took them a while to sort it out.

To European ears, "Castles in Spain/Chateaux en Espagne" is the equivalent of the English expression "Castles in the Air". It's like fairy-tale riches or leprechaun's gold. O'Brian is making a little joke, even though the aforesaid castle is real.

How can he not obtain any advance on funds or why does he have no local friends or contacts

From who?

(in later books he knows everyone) who could take him in?

Well... that's several years down the line.