When I edit a cell, Calc displays an Edit Mode bar that covers adjacent cells. I find this annoying, especially when creating formulas and trying to click those covered cells to insert references. There is already an Input Line / Formula Bar at the top of the window, I don’t need the additional in-cell Edit Mode bar and would like to disable it. Thank you!
Desativar no Menu / Ferramentas / Auto entrada.
Disable it in Menu / Tools / AutoInput.
I learnt a few days ago that the tooltip is only suppressed when you enter the formula for the first time, but not when you edit the cell.
If I understand well, your question is not about the function tooltip,
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but about the formula itself.

Correct. In Tools / Options it’s called “edit mode” (Tools / Options / LibreOffice Calc / General / Press enter to switch to edit mode) - that’s why I called it “edit mode bar”.