How to put the Google search bar widget to the bottom of my Android 10 homecreen?

Nova launcher....

 

the bottom layer being the bottom row of apps on your screen? or the row of icons associated with your back button and app drawer and such?

you can just move the apps one by one up the screen to make room for the search bar. also @Dannydet makes a good suggestion in making nova as your launcher. its a great custom launcher that can customize your phone to the point where it almost feels like a new phone! i highly recommend nova, but there are others you can try ADW is another one to look into.

curious as to what phone you have?

 

No, on most launchers the bottom row is the "dock", a fixed row of icons that stays in place when you swipe between homescreens.
The thing you need to know is that there is no such thing as a "normal" layout for any version of Android. The home screens are provided by an app called a "Launcher", and it's the launcher's capabilities and options that determine how you can lay the screen out, not the Android version or the manufacturer. Different manufacturers bundle different launchers with their phones, but you don't have to use the manufacturer's choice, you can download an alternative and use that.

If you can point us to the page in AndroidCentral where you found that image it might give us a clue as to what launcher they are using.

I just had a quick go with Nova Launcher (my preferred launcher) and was able to place a search widget in (or over) my dock. This doesn't seem quite the same as the shot you included, which looks to me like it still has a dock above the search widget, but it did at least let me put the widget in the place you want. (I've not investigated this before because personally I prefer not to have a search widget at all - I figure I can open a browser when I want to search something).

 

As others have noted, it's your launcher that controls those things. I would suggest looking at Microsoft launcher, they keep it very generic and easy but add a few things like a two row dock if you'd like.