How to manage actions on another site (script)?

Question

Bots

Looked at other services. There is a site with sports predictions, when authorized at a bookmaker (another site), it can automatically place bets on this site, without even opening the tab of the bookmaker, it is enough to simply be authorized on this site (that is, it does certain actions without even showing this, on full auto).
There was this requirement for the purposes.
How can this be done with any website?