I have read that a ROUGH estimate of LED max power use in such fans is 20 mA per LED - that's 0.020 A per LED. The maker claims each fan contains 8 LED's, so that is 0.16 A per fan for lights only, or 1.28 A max total for 8 such fans. No problem for a header able to supply up to 3.0 A.
OP, the specs provided to you by Thermalright tech support are 0.096 A per fan, or 0.012 A per LED. That is less than the guideline I am used to, and MAYBE it is right or MAYBE it is a small under-estimate if they are citing AVERAGE power use, and not MAX. Either way, there is not a problem.
Alternatively, the actual measured values posted by the link provided above says 0.44 A max per fan, quite a bit more (2.5 times!) than that rough guideline. That would make the total for 8 such fans 3.5 A, more than the header can provide. I will comment that the method of power use measurement in that post may not be accurate. What WOULD be more accurate would require some custom wiring fabrication in a cable connecting one fan's lights to a mobo ARGB header. You need to insert into the +5 VDC power supply line a multimeter to measure DC Amps in a range 0-50 mA. Although such a measurement can under-estimate that current slightly (because the ammeter itself imposes a small added resistance in the circuit), such an error is small. And of course, one would need to alter the display type to find the max current for very bright use of all colours.
If you cannot verify the LOWER power requirement and want to be sure the higher value of 3.5 A total is met, you need to use an ARGB HUB like this from Thermalright
https://www.amazon.com/Thermalright-Controller-Support-Magnetic-Suction/dp/B09SLPGJJS/ref=sr_1_33?crid=283YB5GMHI6P2&dib=eyJ2IjoiMSJ9.xZMKqBiTmw4UKGtjNm0BYoYmQFF3s96DVGMOW157oCBT9H9NCGw1t-2sFtqaV_AVdOcjM755DeuVQC-vje_t6VYvKMTq-RqO2fZuMAOO4-Jgu4avjWIoPrcUubmahkNUpWZjNI-ChxoZnxRK176JODw0Ntx-4AMmfy7PTr5DTWt8JWm3bfnNMBVnFYf5EO3yiNRKjmk5ureJ7_m7awugOXMs1n3eFbwtZES0M0LokoQ.qciuMLxMQUag0EcK23yVteGrXL6fB5KQV1uLnj3wUdw&dib_tag=se&keywords=argb+Hub&qid=1720537633&sprefix=argb+hub,aps,100&sr=8-33
It gets the control signals from a mobo ARGB header but draws NO current from that header. Instead all the power for its lights comes from the PSU directly via a cable to a SATA power output from the PSU. That power source can supply up to 4.5 A total load. Note that this is a LIGHTING Hub only. There are now many combo units that have BOTH lighting and fan motor hubs in one box or board, but you do not need that.