Hey there, not an expert by any means, but I was having the same issue and I went to my windows setting (windows 11) and changed the colour of my cursor. Because the although I couldn't see the cursor while typing on Google Docs when something was highlighted, I could see the white "I" over the highlighted text. This just led me to assume that the cursor was just blending into the white page background, which was why I changed the colour of my mouse to pink and voila! problem solved. My cursor has a black border around it now in the Google Docs, which prevents it from disappearing. Hopefully this helps.
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