Hey there Randi,
We do this frequently in our district using Google Sites! You'll want to make sure when you create the game in Gemini that you include in your prompt at the end of it this line so that it's formatted properly for a Google Site: Create a single-file HTML, CSS, and JavaScript code block for Google Sites. From here, once your code is generated, you'll copy it and head over to your Google Site, and here's what I like to do to make it a nice full page embed that looks good for the students to use the activity/game/etc.:
Click on the "Pages" tab and hover over the "Plus" icon in the bottom right corner. Then, select the "Full page embed" option. It'll prompt you to name your page, then click done. From here, select the "Add embed" option and this is where you'll select the "Embed code" option and paste your code from the Gemini Canvas creation into this box, and click next, and then click insert on the next screen.
This will give your students a fully interactive version of the game/activity/experience you designed using Gemini Canvas on the Google Site. Just don't forget your publishing options to ensure they can access the Google Site.