Hi ayulit,
Based on my test and research, I am afraid this is by default that new messages sent to the Groups folder won't trigger a new mail alert.
As a workaround, we may drag the folders under Groups that we need to monitor to the Favorites section at the top of the Mail Navigation (CTRL+1):

So that it can be easier to check the new messages in the Groups folder.
Hope you can find this helpful.
Best regards,
Yuki Sun
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