I see in the source code that you are using the Astra theme, and that the unwanted pagination is generated by Astra.
If you made a custom archive using Toolset, then you should be able to locate the Astra theme settings when editing the custom archive (screenshot) and be able to disable the pagination that way.
I disabled the Astra pagination settings as you indicated but this does not seem logical.
If this is the case, why do the Astra settings for the second site appear "enabled" as well.. but the second set of pagination controls do not display on the frontend?
I'm glad the second set of controls on the first site nolonger show. but the second site should display them as well if the proposed reason were the only cause.