Why should the problem start to appear very soon? Once the /e/-devs start to develop /e/-OS 10 or even 11, they will fork the AOSP/Lineage codebase and adjust the source code to their own needs.
So it doesen’t matter what Google is doing on their side. There will always be calls to Google servers in the AOSP code and also in the Lineage code (as long as Lineage does not focus on being google-free) because they are seperate operating systems and not related to /e/. These calls will then be removed by the /e/-devs when they develop new versions of /e/-OS.
If you for example compare the codebase of /e/-OS pie with the corresponding Lineage version, you will notice that the connectivity check of Lineage still uses Google servers while /e/ uses its own servers. That’s what the devs are calling “Ungoogling” - identifying unwanted google calls in upstream code and removing/replacing them in their own source.