Safari not working properly - all software up to date as of today.

Go step by step and test.

1. Quit Safari, launch Safari holding the Shift key down.

    https://support.apple.com/en-us/HT203987

2. Startup in Safe Mode. https://support.apple.com/guide/mac-help/start-up-your-mac-in-safe-mode-mh21245/mac.  

    Quote:

    It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. 

    And it deletes some system caches, including font caches and 

    the kernel cache, which are automatically created again as needed.

3. Clear History

    https://support.apple.com/guide/safari/clear-your-browsing-history-sfri47acf5d6/mac

    Please read the article before clearing history, 

    this is like a low level resetting of Safari without affecting passwords and bookmarks.

4. If Safari doesn't open a webpage or isn’t working as expected

    https://support.apple.com/en-us/HT204098