The author uses real world ships, including the ocean liners.
So the ocean liners he buys are western ones. IIRC, the hotel one is Royal Caribbean's Oasis of the Seas. (look it up - I guess I can't put a URL tag in a spoiler). Though I think he eventually buys a Japanese liner for the Japanese cuisine.
e.g. Here's the Klugo:
https://www.boatworld.jp/boat/stockList/detail.html?shopNo=278-1&shipNo=48
Here's the Hideaway:
https://orsosisland.com/
And here's the Seeker:
https://www.sunseeker.com/yachts-and-boats/previous-models/155-yacht
I swear this story is the author wanting to own all these ships but being unable to afford them. So he lives vicariously through the MC and pretends to own them (which is fine by me as the story is entertaining).
He's trying not to draw attention to himself. We can debate whether his reasons are valid or not. But that doesn't change the fact that he is trying not to publicly do anything which makes him stand out too much.
Way back when he told the guild he was going to try to reach the southern continent to trade pepper, he was told something like 1 in 3 such voyages ends up with the ship and crew being lost at sea. So it would've been obvious something was strange if he successfully made a dozen such trips when first starting out.
After the war, the "great mage's" ships' indestructible attribute became widely known. And that was when he finally told the merchant guild that he could make trips to the southern continent safely - because his ship was invulnerable.
In the LN, the dark elf island party constitutes him fulfilling his contract obligation with Felicia. And they bang. (It's a fade-to-black type scene though.)
Likewise, him getting the ocean liner (with onboard casino) constitutes fulfilling his contract obligation with Ines.
They just opted to omit it in the manga for whatever reason.