I am occasionally unable to synchronize tasks due to a "dailyLimitExceeded" Google API error. The attached image is taken directly from the app's UI.

Thanks for the report. Google made a change to a response in the Tasks API yesterday that effectively caused Tasks to launch a DDoS attack on the API and exhaust the quota very rapidly
I opened a bug report about that here. I released version 6.6.5 with a fix to handle the change and switched to a new API key, disabled Google Tasks for the previous API key, and waited for the quota reset at midnight. Unfortunately they seemed to be letting the old key continue to make API calls after midnight. I submitted a quota increase request which was partially granted, but the new quota was exceeded by the time I woke up.
They reverted the API change at some point this morning. I answered some of their follow up questions so hopefully they bump up my quota again and Google Task sync will start working later today. If they don't increase my quota some more then it won't start working again until midnight PDT tonight.
Hey, thanks for the quick and thorough reply. Sync still appears to be broken so I'll check again tomorrow morning and report back here. Thank you for being responsive to my concern!
I tested bidirectional sync and it's now working as expected. Thanks again for keeping a close eye on things!
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I tested bidirectional sync and it's now working as expected. Thanks again for keeping a close eye on things!