Install Google Play Services without Google Play Store

Recently, I rooted my phone for the first time, and wanted to get rid of most Google apps including the Play Store. However, after seeing multiple apps didn't work correctly because of a dependency on the Google API, I decided I had to install Google Play Services again.

After installing the latest version from apkmirror, and checking I had the Google Framework installed, apps still crashed and displayed won't run without Google Play services which are not supported by your device. This seems odd as I have Android 9 installed on a OnePlus 6. Is this issue caused by not having the Google Play Store installed? If so, is there any way to circumvent it using another app?

EDIT:

Would I be able to flash GApps on a stock ROM? Also, for some reason, the last time I tried to remove the Play Store I couldn't find its package in the /system folder.
When I tried to flash GApps, it displayed that I already had Google Apps installed. Also, it output Error 70: insufficient memory in system partition.
Also, is there any risk of crashing my OS because OpenGapps would overwrite some of the current stock Google apps?