Short answer: not possible.
This is not possible because the way in which Mac Spaces work and the function you're using are incompatible.
Mac Spaces organise content in different Spaces, and when you go fullscreen, that window gets its own Space.
cmd + ` switches between windows of the same application, but this state is not shared between Spaces.
How to switch between 2 Chrome windows like Alt-Tab in windows?
Worklfow Tip: How to switch between multiple browser windows?
macos - Shortcut for toggling between different windows of same app? - Ask Different
How can you switch between two different windows ...
Videos
Short answer: not possible.
This is not possible because the way in which Mac Spaces work and the function you're using are incompatible.
Mac Spaces organise content in different Spaces, and when you go fullscreen, that window gets its own Space.
cmd + ` switches between windows of the same application, but this state is not shared between Spaces.
Control+→ and Control+← is a default keybinding to switch between full-screen applications on MacOS.
As far as I know, there is not a way to limit it to only Google Chrome.
On Windows I can just Alt+Tab between 2 Chrome windows easily. Example, comparing November reports pages to December for 2 hours.
On Mac there is Command + ` but it keep cycling through all my Chrome tabs. There is also Command + Shift + ` to cycle back, but it hurts my brain and hand. Any suggestions or an app that emulates Windows behavior?
Hey Macs! I've switched to an MacBook Air after using windows for 25 years a month ago and I love it. Great built, battery life, etc. etc. You've heard it before.
There is just one thing I'm missing: Switching between Chrome windows. Chrome is my goto app for basically everything and I find myself copying data into a Google Spreadsheet while taking notes in a Google Doc while researching some stuf every day.
I've set up CMD + ` to toggle between the Chrome windows but its super anoying that CMD + Tab doesnt do the job. Especially since it toggles through them in a static order instead ordering them dynamically by recently used.
Not sure if i be able to work with this long term and there seems to be no solution software wise. So: how do you handle multiple Browser Windows in practice?
UK Keyboard
[see below for other languages]
Cmd ⌘ `
Cmd ⌘ Shift ⇧ ` to go the other way.
Left of z on a UK keyboard [non-shifted ~ ]

Note: This only works if all windows are in the same Space, not if they are spread over multiple Spaces, or if any are fullscreen.
To overcome this for non-fullscreen window, use Cmd ⌘Tab as usual and on the icon of the application you want to switch windows in press the down arrow key (with Cmd ⌘ still pressed). Then use left/right keys to navigate to the desired window across spaces and desktops. To emphasise, This fails for any fullscreened windows, whilst continuing to work for any that are not.
You can also achieve this by right-clicking the app's icon in the Dock - this is the only method that will also switch to fullscreen windows, the other methods will not.
From comments - You can check which key command it is for your language by switching to Finder, then look at the Window menu for 'Cycle through windows'...

BTW, specifically in Chrome, Safari & Firefox, but no other app I know of on Mac, Cmd ⌘ (number) will select individual tabs on the frontmost window.
It also would appear that Cmd ⌘ ` is yet another of those language-specific shortcuts; so if anyone finds any more variants, please specify for which language & keyboard type.
If anybody finds new combos for different languages, please check Keyboard layout here - This is a mirror of the very useful old Apple KB page, now gone from Apple How to identify keyboard localizations - & add that as well as which Input Source you use in System Prefs > Keyboard > Input Sources.
Add a keyboard picture from the KB page too, if that would help.
That will make it easier for future Googlers.
Further info:
You can change the keys in System Settings… > Keyboard > Keyboard Shortcuts… > Keyboard
though it doesn't list the reverse direction, it does still work when you add shift to that new combo. I tested by moving mine from ` (and ~ ) to § (and ± )

You can use the alternative of Ctrl ⌃ F4 [visible in the prefs window above] but that almost indiscriminately marches through every single open window on all Spaces, without switching to the correct Space each time. It's really not too useful unless you use a single Space, just included here for completeness.
On US keyboard:
Next window: Command ⌘ `
Previous window: Command ⌘ Shift `
` is the key on top of Tab key, so it's similar to Command ⌘ Tab shortcut.

On other language:
Go to System Preferences -> Keyboard -> Shortcuts -> on the left menu, select Keyboard -> on the right menu, select Move focus to next window. You can now change the shortcut to which ever key is on top of Tab in your keyboard to work like intended.
Attention:
Doesn't work when window is in full-screen. In that case, you have to use Mission Control shortcuts, e.g. Ctrl ⌃ → and Ctrl ⌃ ←
⌘ Cmd+` works for me with the same versions of Chrome and OS X, so it might be something specific to your installation.
You could try temporarily resetting Chrome's preferences or disabling extensions. Or change the shortcut from System Preferences or test if it works on a different account.
This issue is so annoying for me, and today I finally got it resolved! So, in hope to help some poor soul like myself, I want to share what I did:

- Go to System Preference --> Keyboard --> Shortcuts tab -->
Move focus to next window - Set it to ⌘ + `
Updated screenshots for MacOS Ventura 13.3.1:


The shortcut Command + ` (the key just above the tab key on your keyboard) is the standard Mac OS shortcut for switching between the windows in the currently selected application, and works in Chrome.
Looks like the old COMMAND + ` combo no longer works.
Try control + left/right arrow instead.
Worked on my m1 Macbook pro running macOS Big Sur.