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!