AMD may have an answer to the RTX 3060 Ti, along with other budget cards from NVIDIA. Apparently, AMD is gearing to release the RX 6700 and RX 6700 XT, which will both use its Navi 22 GPUs. The cards will have 12 GB of GDDR6 VRAM too and may arrive as early as January 2021.
https://www.notebookcheck.net/The-AMD-Radeon-RX-6700-and-RX-6700-XT-tipped-to-launch-with-Navi-22-GPUs-with-12-GB-of-GDDR6-VRAM.505945.0.html
RX 6700 looks like a perfect upgrade for me from RX 588 for my 1080p monitor. Even the TDP is slightly lower.