That's essentially a spam protection feature. Because WeChat has so few non-Chinese users, most "foreign" accounts are actually made by spammers. So you're graylisted until they become confident you're an actual human. I've only seen that warning message about an unverified account once among the 100+ foreign WeChat contacts I have (most of them Pakistanis), but I seem to recall that the warning also included an option to verify the contact. Obviously they don't want to give spammers a way to directly verify themselves.

Since 2018,newly created Wechat Account isn't able to login via Web Wechat anymore,using Windows WeChat is ok. If you don't keep your account active everyday through browsing or sending message, WeChat may be lock you out, saying it needs to verify the account.

"The error message just said that for security reasons, only verified accounts were allowed to use WeChat through the web"

If non-verified accounts were to have access to WeChat web, it would be significantly easier for people to operate bots on WeChat personal accounts, by spoofing the client as per this framework:

https://github.com/Chatie/wechaty

Interesting. I connected to my wife (who is originally from mainland China) and her family and I do not think they saw any warnings when chatting with me.