Achieving the “shift-click” moving and remembering the position is a bit complicated.
A fast solution would be to enter this line of code into the chat console:
/run hooksecurefunc("GameTooltip_SetDefaultAnchor", function(tooltip) tooltip:SetPoint("BOTTOMRIGHT", UIParent, "BOTTOMRIGHT", -500, 500) end)
Experiment with the values -500 and 500 until you have the tooltip in a position you like.
You then have to run this line every time you reload the UI. It could also be put in a macro. Or to have it run automatically, put it (without the /run) in an addon e.g. using this addon generator: https://addon.bool.no/