For example, what does the △ mean in C△7?
It's a major 7th chord! C△7 would be C, E, G, and B♮.
The triangle also shows up in a common notation for minor major seventh chords. For example, CmM7 can be written as CΔ̲. The underlined triangle seems to be a combination of the C‒ notation for Cm and the CΔ notation for CM7.
This seems especially common, along with C∅ instead of Cm7♭5 for half-diminished chords, in hand-written charts. Less to write, and less information to process for improvisers reading the through the changes.