Can I put the switch in my menu instead of the corner?

Yes, if your theme has a Menus screen — a block theme has none. Go to Appearance → Menus, open the Dark Mode box on the left and press Add to Menu. It behaves like any other menu item: drag it where you want it, rename it, nest it.

Then, under Toggle Button, turn on Manual placement only so you do not have two switches.

The same button can also go in as a block, as [dark_mode_switch], or as a link in your own template — any link pointing at #dark-mode becomes a switch.

The same box has a Light, Auto and Dark switch: three buttons in the menu in place of a link, where Auto hands the choice back to your schedule or the reader's device. On a block theme, add a Custom Link to your Navigation block pointing at #dark-mode-choice for the same three buttons.