the usage of 'could' in these lyrics

[Sweetpumpkin]

Hello, all you Gosues,

While I listened to the CCM song, 'There is none like you', I got curious the usage of 'could' in the lyrics below:

There is none like You
No one else can touch my heart like You do
I could search for all eternity long
And find there is none like You

Here, I think "could" seems different from the "could" that indicates ability with past tense, like the following sentence: When I left school at 16, I couldn't read or write.
There are many different kind of usage of 'could'. I cannot figure out what it is in this case. Please help me!

Thank you in advance,
sweetpumpkin

[MrPedantic]

Hello SP,

"Could" here indicates "possibility". Thus the phrase means:

1. It would be possible to search for all eternity, and find that there is no one like you.

Cf.

2. I can't come today. But I could come tomorrow.

=

3. It is not possible for me to come today. But it is possible for me to come tomorrow.

All the best,

MrP

[Sweetpumpkin]

Thank you for your quick answer, MrP.

Then, is it right to understand this way?

"Even though I search for all eternity, I will find that there's no one like you in the end."

Thank you in advance,
sweetpumpkin

[MrPedantic]

Hello SP,

Yes, that's the essential meaning.

(I'm a little concerned about your cat, in your avatar. Is it well?)

MrP

[Sweetpumpkin]

Wow, how quick you are, MrP! Thank you again!

As for the cat in my avatar, it is stretched in the picture by Photoshop, not in reality, I'm sure. As far as I know, the picture is an album cover of a Japanese Rock band, 'Spitz'. I should change it sooner or later not to cause concerns.

sweetpumpkin

[MrPedantic]

[Sweetpumpkin]

Okay, MrP. I won't change it!

You have a happy Sunday, too!