It doesn't make any sense for me, why would someone use those very hi fidelity op amps with nothing connected on input and output
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10\$\begingroup\$ Those symbols are there to show the power connections. Other sections of each chip represent the actual amplifiers. Look for matching reference designators that only vary in the last character, such as "U3A" and "U3B". These are all part of the same physical chip, "U3". \$\endgroup\$– Dave TweedJul 13, 2021 at 3:00
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1\$\begingroup\$ Hi Hiro. The answers explain the purpose of the schematic, but to be complete, all those capacitors serve an important purpose: noise reduction. As those op amps draw and release power between the two planes, they cause the voltage on those planes to bounce around. That's undesirable in any circuit, but incredibly undesirable in audio circuits. The caps let the noise pass to ground rather than affecting the supply nodes of the op amps, which would affect the signals they're passing. \$\endgroup\$– JBHJul 13, 2021 at 19:17
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These symbols represent the power supply pins for op amps that are used elsewhere in the circuit. Note the reference designators: U3C, U4C, U8C, and U14C; this means that they are the third sub-unit of each of U3, U4, U8, and U14. Furthermore, note that these sub-units don't have input or output pins. By putting these supply sections separately from the amplifiers themselves, it's possible to make the schematic neater by separating power and signal portions in the drawing (and showing power supply considerations like decoupling in context, as Transistor pointed out in a comment).
Since the NUM4580E and LM562 are dual op amps, for each of these symbols, you'll find schematic symbols showing how the two actual amplifier circuits (U3A, U3B, U4A, U4B, ...) of each dual op amp chip are connected to the signal. They will be elsewhere on the page, most likely in the signal chain, and won't include the power pins but will include the inputs and output. This separation also allows the two amplifiers on each chip to be located in separate locations on the page, if they logically don't make sense drawn right next to each other.
You may also find that in some cases, an op amp is connected "uselessly", e.g. with its inputs tied together or tied to ground. This happens if there are any unused op amps (e.g. seven op amps are needed and there are 8 available), to ensure that they're in a known good state and not floating/oscillating. Texas Instruments has a document about it.
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2\$\begingroup\$ ... and just as important, it shows the location of the decoupling capacitors beside each op-amp. \$\endgroup\$ Jul 13, 2021 at 14:24
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\$\begingroup\$ These chips (1458 and 1462), only have two "real" amplifier subunits. The diagram shows a "fictitious" third subunit with only the power pins connected, plus the bypass capacitors. \$\endgroup\$ Jul 13, 2021 at 18:57