@3X7E 

Thank you for sharing the details!

Here is a newer chipset driver for Archer T3U /T3U Plus, please give it a try and issue will be gone or not. 
https://static.tp-link.com/beta/2021/202101/20210108/RTLWlanU_WindowsDriver_1030.41.0514.2020_Drv_3.00.0036(26078).zip

Here is an instruction to manually install driver: 
https://www.tp-link.com/support/faq/920/

Note: (for test purpose) it is recommended to put the computer closer to the router and shut off some programs like gaming or online video applications while perform ping test.

If still the issue, please help confirm some details here and we would like to escalate your case: 
1.How did you do the ping test and please share photo of the ping:
2.  When the ping spikes appeared, what are your network activities, for example playing online games, video streaming or P2P downloading, etc? 
3. May I know  the model of the router, does the issue happen particularly on 2.4/ 5Ghz WiFi?
4. How about the other wireless adapters, does other pc or laptop work fine with the same Wi-Fi?
5. Please check the motherboard of your computer and share a photo with us: https://www.tp-link.com/support/faq/2722/