Do I need to worry about EMI/RFI/etc. for 110V and 12/5V electronics in the same electric panel?
I suggest you use STEEL construction, for the magnetic shielding that material can provide.
Especially with thermocouples --- 40 microVolts per degree C --- you don't want spikes from motors, or microwave ovens, or light switches, or even the
interference from 10 ampere 60Hz power cabvles.
How bad can this be? We compute thusly
Assume 10 amps at 60 Hertz.
The dI/dT = 10amps * 377 radians/second
= 3,770 amps per second.
Assume a distance between the power wiring and the thermocouple wiring of 4&quot; (10 centimeters). Assume the vulnerable cross_section of the thermocouple wiring is 4&quot; region by 1mm wire_to_wire spacing.
We use the merged version of Biot_Savart and Faraday Law of Induction, for couipling between a rectangular circuit vulnerable to magnetic field, and a long straight wire &quot;transmitter&quot; positioned to be co_planar with our rectangular &quot;receiver&quot;.

V_induce = [ MU0 * MUr * Area / (2 * PI * Distance)] * dI/dT

where Area is the receiver rectangular loop (rectangle, for easy computation)
and Distance is between the Wire and the Loop (we ignore complex geometries here, because we want an order_of_magnitude of V_induce)
Using MU0 = 4 * PI * 1e-7 Henry/meter, and MUr = 1 (copper, aluminum, FR-4,air)
we simplify to

V_induce = [ 2e-7 Henry/meter * Area/Distance ] * dI/dT

Remember this is for a CLEAN SINUSOIDAL POWER LINE WAVEFORM, no spikes from motor commutators, no rectifier surges from microwave ovens.

V_induce = 2e-7 * (10cm/1mm)/10cm * 3,770   answer in volts

V_induce = 2e-7 * 1mm * 3,700 = 2e-7 * 3.77 = 0.8 microVolts


With NO SPIKES, 4&quot; separation form power cables and thermocouples.
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Howeer, rectifier spikes in your power supplies can easily be

1 amp average (100 watt power supply), 10 amps peak (easily) in 10 microSeconds if little EMI suppression inside that (cheap) power supply

Thus the dI/dT of power supplies is easily

10 amps rising in 10 microseconds, or 1 Million amps per second

Notice the 1Million, compared to the pure sinusoidal 3,770 (10 amps clean power) is 250X larger coiupling, or 250 microVolts.
Thus the thermocouple interferer went from 0.8 microVolts to 250 microVolts.
And this ignores electric field coupling.
**** people will argue, rightly so, that twisted pairs in power cabling (HOT twisted with RETURN) reduces the aggressor fields. And people will argue that twisted pairs of the Thermocouple wires will reduce vulnerability to the aggressor fields. I agree. But sloppy, irregular, slow_rate_of_twisting will not provide these benefits.
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Power supplies will be switch_mode, for &quot;efficiency&quot;, but that becomes useless when you need massive EMI/RFI filtering to have successful sensors/wiring near these supplies.
Within the supplies will be 200 volt/100 nanosecond nodes (drains of power MOSFETs) that must be heatsinked (perhaps 5% loss, via heat, plus a baseline charge switching heat_loss), and these 200volt/100nanosecond nodes will couple to the OUTSIDE thru any little gaps in the cases of these power supplies.
Thus electric fields will be a problem.
Expect to need a partition between the high_voltage region and the sensor wiring.
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Also read and understand the BobFlux answer.