I cannot open webarchive files any more

I duplicated your problem by creating a webarchive in Safari and when I double-clicked it. I received the error "macOS cannot verify that this app is free from malware". I then went to System Preferences -> Security & Privacy -> General tab and there is a message from GateKeeper (a macOS anti-malware system) advising me that the filename was blocked from use because it is not from an identified developer and there is an Open Anyway button.

An alternative to using the Open Anyway button is to simply, right-click the file and choose Open and either way, the flag that prevents opening this file will be cleared. It will be remembered and you won't have any trouble double-clicking the file in future. Every new webarchive you create will need this step performed.

This has to do with Gatekeeper security in macOS and the behavior is by design. Someone could craft a malicious webarchive file. The error means that to avoid webarchives being blocked they need to be signed (and possibly submitted to Apple to verify there is no malware included a process known as Notarization) by a paid developer account. You would only need to do that if you plan on distributing the webarchive to other Mac users.

You may find saving to PDF to be more useful than using a webarchive. But you may have good reason to use the webarchive format.

This explains how this works for Apps. Apparently, a webarchive is considered just as dangerous as an App. It can contain executable code such as JavaScript and there must have been some security issues with webarchives in the past for Apple to block the files in such a manner.

https://support.apple.com/en-us/HT202491