Gwern’s tips for “quick searching” (which I implement using DDG !bangs and Firefox Saved Searches) are very useful too, when you know you’ll use a website regularly, I have about 30 custom saved searches now.
It came with a bunch of built-in web search keywords that sped up your search intents (all customisable of course). Usually two or three letter prefixes, that were terminated by a colon, so you could, f.e. 'ggl: khtml history' (takes you direct to first google 'lucky' result) or 'wp: charles eaton' (search and show wikipedia's top hit for charles eaton), etc.
[1] https://addons.mozilla.org/en-US/firefox/addon/gesturefy/
These hotkeys are functionally the same as Ctrl+Tab and Ctrl+Shift+Tab, which - at least in my idle position - don't require moving your hands any meaningful amount.
If your hand is on your mouse, though, this means you don't have to move that hand back. (I'm assuming left-hand mouse uses won't find anything involving TAB to be hand-agnostic. : )
My usage pattern tends to be keyboard - search, tune search - then mouse - open lots of new tabs, then scroll up / down with mouse, and flick between those new tabs with the mouse, perhaps select some text with the mouse.
I think everyone agrees that frequent relocation between mouse / keyboard is sub-optimal.
If you have a mouse with some additional side buttons (that you don't already have mapped) I can strongly recommend mapping them to ctrl-pgup and ctrl-pgdn, so you can go left/right with your tabs in the current browser without having to relocate either your hands or your mouse pointer. Because I tend to open many links to new tabs (middle-click) - a consequence of living in a country (Australia) with poor internet speeds - I'm now lost whenever I have to use a mouse without those buttons.
Watching people use the mouse to go to the hamburger menu to recover a just-closed-tab, or to the tab bar to switch between tabs, or moving the mouse to the scrollbar to move the content up/down, is the contemporary equivalent of watching someone play Solitaire intentionally poorly.