User experience between disparate systems

I have two “My Account” sections of the same website. Our’s is a library website and has an integrated search tool. The search tool is a vended solution and has the ability for the user to log in and access account information, set personal settings, etc. The front-end UI for the search tool has been customized to look and feel like the library’s website. When the user does a search from the library website, the results open up into a new page that looks a lot like the library template but is actually a disparate system. The library website is react-based. The search tool is built with Angular.

This has created a somewhat troubling user experience. If you log into the library website you are presented with “My Account” options. Then, perform a search, and now you are presented as logged out and with a whole new set of “My Account” options when after you log back in.

I’ve been tasked to present options as potential solutions for this troubling user experience and thought I would through it out here, to the community, for suggestions or if someone else has tackled a similar UX issue, how was it handled?

Thanks in advance for your time!

If you can share picture of the screen, hand drawn screen or any thing similar will be helpful