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From Did Gandalf know the origin of "Glamdring"? we learn that Glamdring belonged to the King of Gondolin (Turgon) and that Elrond suspects it was looted from the remnants of the city by orcs or dragons.

Rivendell was founded by Elrond and other survivors/descendants of Gondolin. Elrond's father Eärendil was born in Gondolin, and King Turgon was Elrond's great grand-father. Legally, Glamdring would actually belong to Elrond by right of heritage, Elrond being Turgon's closest living relative in Middle-Earth.

Also, the sword belonged to the former High King of Noldor, so having it in his possession would strengthen Elrond's position and claimed heritage from a political point of view. Much like Narsil did for Aragorn.

Yet Elrond lets Gandalf have the sword almost dismissively!

Sure, he might think that Gandalf has greater use for it, just like Cirdan thought Gandalf would have greater use of the ring Narya. But he doesn't even seem particularly surprised or even excited upon encountering an old heirloom of his own family, which has been lost for several millennia.

Seriously!?

Compare this with with Elrond's fascination over the sword Narsil, and his bland reaction upon finding Glamdring seems even stranger.

And then Gondolin was located in the old world, supposedly somewhere vaguely far north of Rivendell. If the swords were originally looted by orcs/dragons, then carried around all over the world in various loot piles for two ages, isn't it a strange coincidence that they are found so close to Rivendell?

I am aware that these swords (Glamdring and Orcrist) are kind of an anachronism, as Tolkien borrowed bits and pieces from The Fall of Gondolin in his latter works. But perhaps there exists a canonical explanation, a 'patch' released by Tolkien afterwards, like in the case with the Glorfindel anachronism in LOTR?

Elrond recognised that Glamdring and Orcrist were both forged in Gondolin and that Glamdring belonged to the King of Gondolin (who is not named).

They are old swords, very old swords of the High Elves of the West, my kin. They were made in Gondolin for the Goblin-wars. They must have come from a dragon's hoard or goblin plunder, for dragons and goblins destroyed that city many ages ago. This, Thorin, the runes name Orcrist, the Goblin-cleaver in the ancient tongue of Gondolin; it was a famous blade. This, Gandalf, was Glamdring, Foe-hammer that the king of Gondolin once wore. Keep them well!

_{The Hobbit Chapter 3: A Short Rest
Page 48 (Unwin Books 1966 paperback edition)}

Unlike Aragorn, Elrond did not need proof of his lineage, and in any case he would not try to make his guests give up their finds just because they once belonged to his family.

I don't think Elrond was particularly fascinated with Narsil. After Isildur was killed, Elrond helped to pass its shards on to each of the heirs of Elendil. He understood its significance in Arnor and Gondor and arranged for it to be reforged so that Aragorn could take it with him when he left Rivendell with the Fellowship.

In The Hobbit, Elrond is identified as a half-elf but not as a descendant of Turgon:

The master of the house was an elf-friend - one of those people whose fathers came into the strange stories before the beginning of History, the wars of the evil goblins and the elves and the first men in the North. In those days of our tale there were still some people who had both elves and heroes of the North for ancestors, and Elrond the master of the house was their chief.

_{The Hobbit Chapter 3: A Short Rest
Page 47 (Unwin Books 1966 paperback edition)}

If we step outside the bounds of cannon, it is possible that, when he wrote The Hobbit, Tolkien had not yet decided on Elrond's exact ancestry. However, even within canon, I think Elrond's behaviour is not inconsistent.

As to two swords from Gondolin being found so close to Rivendell and very many miles east of where Gondolin once stood (in Beleriand - which by this time was under water), I agree that it seems to be a coincidence. It is possible that they were both taken at the same time and so happened to stay together over the millennia because they passed together from one owner to another.