Welcome to Android Central! It's important to know which Android version you're using, because from Nougat through Pie, Android System Webview was disabled by default, since Chrome functioned as the webview app in those versions. Starting with Android 10, ASW was re-enabled.
Also, I've seen it where the Play Store can't update both at the same time -- i.e., if Chrome is being updated, you can't also select ASW to be updated. If you were to tap the Update button for ASW, then Chrome would suddenly stop updating. I'm not sure why that happens, but the thing to do is to just let whatever is updating finish, and then tap the Update button again.