I do all my zypper ups with all web browsers closed, usually either first exiting X before zypper up, or restarting X afterward, when the up did not include new kernel or other reason to restart the entire OS. All my browser profiles are configured to pickup where left off.
I did such a procedure today, and Chromium was upgraded from 125.0.6422.141-bp155.2.91.1 to 126.0.6478.182-bp155.2.99.1. Its existing tabs for my two webmail tabs and for the 8 forums tabs passively object to loading the content that was there when browser was last closed. I must make each tab error and dismiss the error before choosing a selection from right-clicking the back button that will respond as expected. Otherwise, Chromium ignores reload button clicks, and maintains a nothing done, nothing expected, current tab empty of content is perfectly OK state.