A permanent teleportation circle is not a teleportation circle spell
There are some subtle clues in the phrasing of the spell teleportation circle that tells us that the spell teleportation circle and the object 'permanent teleportation circle' are not the same thing.
Firstly, spell names in the text are always in italics. However, the PHB does not say "permanent teleportation circle", but "permanent teleportation circle" without italics. This suggests that a permanent teleportation circle is not a teleportation circle spell with permanent duration but rather something different.
Secondly, the wording in creating a permanent teleportation circle differs from other spells which can be made permanent.
You can create a permanent teleportation circle by casting this spell in the same location every day for one year.
Compare with forbiddance,
If you cast forbiddance every day for 30 days in the same location, the spell lasts until dispelled
And Mordenkainen's Private Sanctum,
Casting this spell in the same spot every day for a year makes this effect permanent.
Or Druid Grove (XGtE),
If you cast this spell in the same area every day for a year, the spell lasts until dispelled.
Or Temple of the Gods (XGtE),
Casting this spell on the same spot every day for a year makes this effect permanent.
Unlike these other spells, teleportation circle does not say 'this spell becomes permanent' or anything along those lines. Rather it says that it creates a permanent teleportation circle.
The spell text for teleportation circle describes what a permanent teleportation circle is. They have unique sigil sequences which can be memorised. They are destinations for teleportation circle spells (and other teleportation spells as described in their own descriptions). They can be created by casting teleportation circle in the same location every day for a year. The rules don't say that permanent teleportation circles do anything other than these things - anything beyond these things is inference.
If you read "permanent teleportation circle" as a teleportation circle spell with duration of Permanent, then you open the question of "where does it teleport to?" which produces all kinds of confusion. However, if you take the care to realise that "permanent teleportation circle" is not a teleportation circle spell but rather a separate but related entity, with a confusingly similar name but very different effects, then all the logical headaches go away. A permanent teleportation circle is a destination, nothing more.