No, you do not need to ground the aluminum plate.
The Mean Well is supplying filtered DC power. There is nothing to radiate.
Basically the only possible source of ESD would be the Mean Well CLG and it's enclosed in an aluminum box. Nothing will be radiating from the CLG. Mean Well suppresses the ESD from going back down the power line.
You do not need ESD protection. Even if there was an RF signal on the strips they are mounted to a plate of aluminum that would suppress any ESD.
You are not using lethal voltages so no safety risk.
END OF UPDATE
An aluminum plate will not dissipate much heat. It will absorb heat until it reaches nearly the same PCB temperature as without the plate. Aluminum has good thermal conductivity but not so good convective characteristics without fins. Natural convection relies on buoyancy and gravity (Grashof number) which is minimal on a horizontal flat surface. Unanodized aluminum has poor emissivity and therefore poor heat transfer by radiation.
Rather than use a flat sheet checkout heatsinkusa.com. They have 1" wide heatsinks for 16¢ an inch.
What I do is adjust the current so the PCB temperature is below 55°C (hot to the touch but not burn).
There are some strips with an efficacy of about 180 lm/W that do not need a heatsink. I would guess your strips are about half as efficient, maybe 90m/W.
Also if you were to use strips with more efficient LEDs more of the electrical watts would be dissipated as light rather than heat.
The strips I like are Bridgelux EB-Series Gen 2. when in stock the price starts at $4 per 280mm (11"), 1200 lumen and are also sold in lengths of 560 mm and 1120 mm. The 280 mm strips are 19.5V and the others are twice that.
Samsung has their F-Series Gen 3 strips at the same lengths and similar cost per lumen and efficacy. The Samsung, with more lumens per strip, can be driven to the point where a heatsink is required but I just decrease the current to the desired temperature.
This is a fixture with seven 22" (560mm) using Bridgelux BXEB-L0560Z-30E2000-C-B3 @ $7.41 each.
I have two of them with the strips wired in parallel (driver: Mean Well HLG-185H-48B) and series (HLG-240H-C1400B).
The parallel strips did not balance well. Current in each strip ranged from 800mA to 1500mA. The good news was even at the 1500mA (60W) strip did not need a heatsink. Max rated current is 1400 mA.
This is a project to experiment with growing seedlings under 3000K (BXEB-L0280Z-30E1000-C-B3) and 5700K (BXEB-L0280Z-57E1000-C-B3) $4 strips.
The LED drive is mounted to the top of a wooden shelf and the strips to the bottom. Tomato plants prefer warm 3000K a lot more than cool 5700K.
The PCB I made to set the HLG-40H-54B's current and do power distribution.
Two $14.48 each, 4500 lumen, Samsung 560mm strips P/N SI-B8T261560WW.
No heatsink required under 1 Amp (1.12 Amp max), 25 Watts each.
The 24V is not divided into two 12V rails.
The voltage of an LED is determined by current and the LED's forward voltage characteristics, not the applied voltage.
White LEDs, driven at ≈60 mA, have a forward voltage of about 2.8V.
6 LEDs in series will be about 6 x 2.8v = 16.8V.
A 120Ω resistor would mean there is 60 mA flowing through each LED and resistor.
This works out to 1.44 W per sets of 6 LEDs.
If the above is true the LEDs would be spaced at about 6 mm (160/m) which would add up to 24 W per meter.
The maximum electrical efficiency would then be 70%. The resistors dissipating the other 30%.
Why they do this is a mystery. They could power 8 LEDs per 27Ω resistor and get 93% efficiency.