Daily re-prompted to sign into 1Password in the browser even though only using Chrome extension

There are 3 major clients of 1Password you might not realize as such. The first one is the website 1password.com, which you call "1Password in the browser". The thing it can do best and no other client is managing your account (billing, and in case you have family account, members). For all other uses, use one of the other clients. It's inferior with managing items.

The second client is the desktop app. The thing it can do best is managing, sorting and editing your items. And it is a persistent anchor for 1Password unlock. So do install the desktop app and keep it running in the background. Use it for daily work with editing and managing items.

The third client is the browser extension. The thing it can do best is autofill website logins. It can inherit the unlock from the desktop app, so integrate it with the desktop app and you will manage your unlocks only within the desktop app. By integrating with the desktop app, the browser extension unlock will survive browser restarts, and you have only one single point of unlock timeout for both the extension and the desktop app. Don't use the browser extension to search, manage and edit items. It's basically only for reading items and autofill.

From my point of view as 1Password user since 3 years, you get the best experience by using the desktop app as main 1Password app for managing your items and daily work. It will also integrate with Windows Hello, so you can use your Hello pin to unlock and don't need to always enter your account password. Use the browser extension to autofill, and use the website only once per year to check your billing.

Use the website only, if you need to manage your account, e. g. billing. For everything else, use the desktop app. Change your workflow and consider using the desktop app instead of the website. It's much more comfortable.

If you do it this way, and use Windows Hello, you are prompted to unlock 1Password with the Windows Hello Pin when you're logging in to your Windows PC, then never again until the next login (and of course according to what you additionally set for the PC idle behavior in the desktop app's Settings > Security).