Looks like duplex LC at the bottom, ST at the top.
Likely single mode fibre with the yellow jacket. Multi mode tends to be orange for OM1 or 3, and aqua for OM4. Single mode is 9 micron core, multi mode is 50 or 62.5 micron core. The stuff used in the Toslink system is 1mm plastic fibre.
As to telling the difference, LC and SC are latching connectors, FC is screw on, and ST is an old bayonet connector.
Value of the patch panel, pretty much zero. Unless your NAS has single mode interfaces, it’s not very useful to you.
The distance limitation for high speed transmission (10Gbit/s) in multi mode fibre is modal dispersion rather than loss, but this is likely single mode.
I work in fibre….