ixBrowser have a well documented API and I myself use it in BAS but only for creating new profiles, doing batch updates or loading cookies into the profiles. If you want to completely control the browser from BAS I don't think it's possible or at least you don't need BAS for it.
Curl Impersonate Bas Developer Needed
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Looking for a bas developer that can work with this bas module https://community.bablosoft.com/topic/30528/http-client-curl-impersonate-2-0-http-2-tls-1-3-ja3/2
Text me on telegram @danielmadisonboss