Hello @Radim H - Thanks for raising your issues.
I hope you have followed below documentation to create the connector:
https://learn.microsoft.com/en-us/microsoftteams/platform/webhooks-and-connectors/how-to/connectors-creating
Could you please check if your connect is enabled or not: https://learn.microsoft.com/en-us/microsoftteams/m365-custom-connectors#enable-or-disable-connectors-in-teams
If possible, could you please share the error logs and let us know if it is working in any Teams clients?