Every time I update, the 1Password icon becomes the old one

The blue icon is only used by beta and nightly versions of 1Password in order to make it easier to differentiate them from the stable/release versions that use the icon of your first screenshot.

Thanks for showing me how it works!
I was able to change the icon by holding down Shift and right clicking on the taskbar!
SOLVED!

Hi @poconi, I'm glad to hear that the information provided by viswiz (thanks for the assist!) was helpful, and thanks for sharing your solution 😄

If you have any further questions or concerns, don't hesitate to reach back out!