I’m in the exact situation you’re in. I have the GTi13 + pro ex dock, and an RTX 3080, and I don’t turn the dock on all the time. You have to use two cables, one from monitor to GTi13 (HDMI), and one from monitor to the 3080 (DP) AT The SAME Time.
And in the bios, I selected HG for “hybrid gfx” instead of Auto.