How to stop Google from thinking Edge is outdated version of chrome?

BulletRouge  What you are been seeing is almost certainly a hijack. Here's a similar banner (one among many on the internet in articles discussing this sort of thing) from Chrome that is a hijack:

Although popups are more common, banner hijacks are also common.  The removal steps are, as I understand it, the same in each case.

The standard steps to remove the hijack are:

(1) Turn Off Sync - Turn off sync if you are using it on the affected computer/device. If you have more than one affected computer/device that is infected, turn of sync on all until all have been cleared.

(2) Uninstall PUPs - Open Control Panel and look at installed programs. If you see anything that you can't account for having installed, PUPs might have installed through a program you added. Typically, PUPs purport to be shopping/search programs and/or file management utilities. Do an internet search on any programs you don't recognize to see if the programs are identified as problematic. Remove any programs that are identified as problematic.  In recent years extensions have also become a PUP carrier, so check those as well, particularly any that did not come from Microsoft (numerous bad actors among Chrome store extensions have been recently identified).

(3) Run Anti-Virus/Anti-Malware - Open Windows Security and run a FULL scan (not a quick scan). If you use other/additional anti-malware programs**, run them with a full scan as well. Remove any threats that are identified.

(4) Reset Edge to Default - If (2) and (3) don't resolve the issue, then reset Edge ("Settings", "Reset Settings") to default. Resetting Edge will reset the startup page, new tab page, pinned tabs and search engines, disable all extensions and clear temp data, cookies, history and the like.

(5) Turn On Sync -- After you've cleared all computers/devices that are infected, turn sync back on.

Good luck.  I've not personally dealt with a banner hijack, but but I've dealt with numerous popup hijacks on friend's computers, and I think that this will work for both banner and popup.  If these steps don't work, you will need to dig deeper, possibly into the registry.  If the problem is that deep, a Windows clean reinstall might be the best solution.  I've had to do that, too, in one case where I was cleaning a friend's computer from the one of the PC support scams that got deep into his system.  Ugly, but 100% effective so long as you don't immediately reinstall the cruft.

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** I personally rely on Windows Security as my primary defense, with Malwarebytes Premium as a heuristic overlay, on my production computers, and use Windows Security with the free version of Malwarebytes installed for scanning, if needed, on test/non-production computers.  I'm not sure that it makes a lot of difference; I'm sure that any of the reputable anti-virus/anti-malware products will work.  Use what you use.