Hi Fabien Donnet,
I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to accept the answer.
Issue:
Hello,
I cannot delete my resource:
Unkown error in Azure and "is busy with another operation" with the az cli....
How I can debug.
I can start/stop the resource but I m not able to remove it.
Solution:
The only solution was to contact the support, to be able to delete the stuck Postgres DB and VNet, it takes ~1 month for the support team to unlock my resource and after that I was able to delete the entire RG.
If I missed anything please let me know and I'd be happy to add it to my answer, or feel free to comment below with any additional information.
Hope this helps. Do let us know if you have any further queries.
If this answers your query, do click Accept Answer
and Yes
for was this answer helpful. And, if you have any further query do let us know.