Finally got a real accurate translation of Kon's character song:https://pastebin.com/PN5K43NA
So, the title of the song and in the first half she's obviously singing about wanting to be fifteen years old and finding that special person to love.
Then in the second half she finally found that person, but it only becomes clear who she's talking about until she says:>Even when I placed my dreams on the>dark, dark moon behind the clouds with you>The wind blew reassuringly>forever and forever
Which is a direct reference to this scene in the webm, right when she says forever, the wind blows. I knew this was my favorite scene in the anime for a reason.
Then we have:>With you I can swim through the>twinkling world
Which a reference to the Spring Séance, that "twinkling" world only appears when she does it with Chiya.
Let's go back up:>I could not have found>the world that opened up when I met you, by myself
Now that we know the "world" refers to what they saw in the spring, this part talks about how Kon wouldn't be able to see it without finding that person, aka Chiya. Only Chiya can see this world and help Kon see it.
So now that's clear she's singing about Chiya, all the other dialogue about nights can be deduced to be references to other scenes in which she watched the night sky with Chiya. The only thing I don't get is this four bonds connecting them, and why two of them are filled with kindness and the other two make her heart collapse. But it doesn't matter that much, just with everything above, this is clearly a love song from Kon to Chiya.