I disagree with Dekkadeci answer's. Instead:
BbM7/C would be a proper and more understable name. Or maybe F11/C, which will gracefully accept the following note E.
Look at the two other chords they are: Bb/C and Gm7/C.
That C13 candidate does not contain a single note from the C Major triad indeed: no C, no E no G in the chord. Only a lasting bass, that lasts during all the harmonic evolutions. Before and after.
However it easily could have. On the keyboard there's plenty room to play a E with middle finger, or G besides the A.
When that E is played just after the so-called C13, it doesn't sound like a stabilization to my hear. I insist:
One argument in the other answer is the presence of the E at the late end just before the start of a new phrase: When I play the extract, that E is nowhere near a stabilisation of any sort to a C chord, whehter it be C, C7, C9, C11, or C13. It rather introduces interrogation, lack of equilibrium and asks for the new phrase that starts just after.
There's no reason to name it a C chord, except for the droning C during all of the excerpt, whatever the other chords are playing too.
That long echoing C bass, is also translated in the BbM7/C or F11/C chord. But although it lasts the whole excerpt, I do not feel that C at all like the tonality. Not at all.
And it's because of that "Not At All" that I write this answer. And I strongly suggests the reader to play these notes on a keyboard to understand that it is not a stabilization on any form of altered C major chord.