Messages go to my old provider, or sending fails with error 131070.
Meta's Conversation routing still makes your old provider the primary partner; set WASync as Primary in Meta Business Suite, or remove the old partner.
This happens to a number brought from another provider when Meta's Conversation routing is on for it and the old provider is still its primary partner. The number shows as connected in WASync, but Meta hands every conversation to the old provider: customer messages do not arrive in WASync, and what you send fails with error 131070 ("another app is controlling this thread"). Reconnecting or re-registering the number does not change it; the setting is yours, at Meta.
WASync checks this after the move and several times a day, and shows a red warning on the number in Connections when it finds it. To fix it: in Meta Business Suite → Settings → WhatsApp accounts, select the number, open Conversation routing and set WASync as Primary for Customer service, Click-to-WhatsApp ads, Utility, Marketing and Calls, and as the Escalation partner. If you no longer use the old provider, you can remove it under Partners or Messaging accounts instead. The warning clears itself at the next check.